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(5)Example 1 Mark on the diagram the set corresponding to (A ∩ B0

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(1)

Sets

Tomasz Lechowski Maths Studies September 30, 2017 1 / 12

(2)
(3)

Example 1

Mark on the diagram the set corresponding to (A ∩ B0) ∪ C .

Let’s make some observations:

(A ∩ B0) is everything in A and not in B.

C is of course everything in C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets.

Tomasz Lechowski Maths Studies September 30, 2017 3 / 12

(4)

Mark on the diagram the set corresponding to (A ∩ B0) ∪ C .

Let’s make some observations:

(A ∩ B0) is everything in A and not in B.

C is of course everything in C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets.

(5)

Example 1

Mark on the diagram the set corresponding to (A ∩ B0) ∪ C .

Let’s make some observations:

(A ∩ B0) is everything in A and not in B.

C is of course everything in C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets.

Tomasz Lechowski Maths Studies September 30, 2017 3 / 12

(6)

Mark on the diagram the set corresponding to (A ∩ B0) ∪ C .

Let’s make some observations:

(A ∩ B0) is everything in A and not in B.

C is of course everything in C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets.

(7)

Example 1

Mark on the diagram the set corresponding to (A ∩ B0) ∪ C .

Let’s make some observations:

(A ∩ B0) is everything in A and not in B.

C is of course everything in C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets.

Tomasz Lechowski Maths Studies September 30, 2017 3 / 12

(8)

Mark on the diagram the set corresponding to (A ∩ B0) ∪ C . Answer:

(9)

Example 2

Mark on the diagram the set corresponding to (A ∪ B)0∩ C0.

Let’s make some observations:

(A ∪ B)0 is everything outside of A and B. Using symbolic logic we could read this as: it is not true that it is in A or in B.

C0 is everything outside of C . In logic this is not in C.

Finally we have ∩ between these, so we want elements that are in both sets. Using symbolic logic we have it is not true that it is in A or in B and it is not in C.

Tomasz Lechowski Maths Studies September 30, 2017 5 / 12

(10)

Mark on the diagram the set corresponding to (A ∪ B)0∩ C0.

Let’s make some observations:

(A ∪ B)0 is everything outside of A and B. Using symbolic logic we could read this as: it is not true that it is in A or in B.

C0 is everything outside of C . In logic this is not in C.

Finally we have ∩ between these, so we want elements that are in both sets. Using symbolic logic we have it is not true that it is in A or in B and it is not in C.

(11)

Example 2

Mark on the diagram the set corresponding to (A ∪ B)0∩ C0.

Let’s make some observations:

(A ∪ B)0 is everything outside of A and B. Using symbolic logic we could read this as: it is not true that it is in A or in B.

C0 is everything outside of C . In logic this is not in C.

Finally we have ∩ between these, so we want elements that are in both sets. Using symbolic logic we have it is not true that it is in A or in B and it is not in C.

Tomasz Lechowski Maths Studies September 30, 2017 5 / 12

(12)

Mark on the diagram the set corresponding to (A ∪ B)0∩ C0.

Let’s make some observations:

(A ∪ B)0 is everything outside of A and B. Using symbolic logic we could read this as: it is not true that it is in A or in B.

C0 is everything outside of C . In logic this is not in C.

Finally we have ∩ between these, so we want elements that are in both sets. Using symbolic logic we have it is not true that it is in A or in B and it is not in C.

(13)

Example 2

Mark on the diagram the set corresponding to (A ∪ B)0∩ C0.

Let’s make some observations:

(A ∪ B)0 is everything outside of A and B. Using symbolic logic we could read this as: it is not true that it is in A or in B.

C0 is everything outside of C . In logic this is not in C.

Finally we have ∩ between these, so we want elements that are in both sets. Using symbolic logic we have it is not true that it is in A or in B and it is not in C.

Tomasz Lechowski Maths Studies September 30, 2017 5 / 12

(14)

Mark on the diagram the set corresponding to (A ∪ B)0∩ C0. Answer:

(15)

Example 3

Mark on the diagram the set corresponding to (A ∩ B) ∪ C0.

Observations:

(A ∩ B) is everything that is both in A and in B.

C0 is again everything outside of C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets. Using logic we have it is both in A and B or it is not in C.

Tomasz Lechowski Maths Studies September 30, 2017 7 / 12

(16)

Mark on the diagram the set corresponding to (A ∩ B) ∪ C0.

Observations:

(A ∩ B) is everything that is both in A and in B.

C0 is again everything outside of C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets. Using logic we have it is both in A and B or it is not in C.

(17)

Example 3

Mark on the diagram the set corresponding to (A ∩ B) ∪ C0.

Observations:

(A ∩ B) is everything that is both in A and in B.

C0 is again everything outside of C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets. Using logic we have it is both in A and B or it is not in C.

Tomasz Lechowski Maths Studies September 30, 2017 7 / 12

(18)

Mark on the diagram the set corresponding to (A ∩ B) ∪ C0.

Observations:

(A ∩ B) is everything that is both in A and in B.

C0 is again everything outside of C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets. Using logic we have it is both in A and B or it is not in C.

(19)

Example 3

Mark on the diagram the set corresponding to (A ∩ B) ∪ C0.

Observations:

(A ∩ B) is everything that is both in A and in B.

C0 is again everything outside of C .

Finally we have ∪ between these, so we want elements that are in at least one of the two sets. Using logic we have it is both in A and B or it is not in C.

Tomasz Lechowski Maths Studies September 30, 2017 7 / 12

(20)

Mark on the diagram the set corresponding to (A ∩ B) ∪ C0 Answer:

(21)

Example 4

Mark on the diagram the set corresponding to (A ∪ B) ∩ (C ∩ A).

Let’s make some observations:

(A ∪ B) is everything in A or in B.

(C ∩ A) is everything in C and in A.

(A ∪ B) ∩ (C ∩ A) is everything in both of the above so in A or in B and in C and in A.

Tomasz Lechowski Maths Studies September 30, 2017 9 / 12

(22)

Mark on the diagram the set corresponding to (A ∪ B) ∩ (C ∩ A).

Let’s make some observations:

(A ∪ B) is everything in A or in B.

(C ∩ A) is everything in C and in A.

(A ∪ B) ∩ (C ∩ A) is everything in both of the above so in A or in B and in C and in A.

(23)

Example 4

Mark on the diagram the set corresponding to (A ∪ B) ∩ (C ∩ A).

Let’s make some observations:

(A ∪ B) is everything in A or in B.

(C ∩ A) is everything in C and in A.

(A ∪ B) ∩ (C ∩ A) is everything in both of the above so in A or in B and in C and in A.

Tomasz Lechowski Maths Studies September 30, 2017 9 / 12

(24)

Mark on the diagram the set corresponding to (A ∪ B) ∩ (C ∩ A).

Let’s make some observations:

(A ∪ B) is everything in A or in B.

(C ∩ A) is everything in C and in A.

(A ∪ B) ∩ (C ∩ A) is everything in both of the above so in A or in B and in C and in A.

(25)

Example 4

Mark on the diagram the set corresponding to (A ∪ B) ∩ (C ∩ A).

Let’s make some observations:

(A ∪ B) is everything in A or in B.

(C ∩ A) is everything in C and in A.

(A ∪ B) ∩ (C ∩ A) is everything in both of the above so in A or in B and in C and in A.

Tomasz Lechowski Maths Studies September 30, 2017 9 / 12

(26)

Mark on the diagram the set corresponding to (A ∪ B) ∩ (C ∩ A). Answer:

(27)

Example 5

Mark on the diagram the set corresponding to (A0∩ B0) ∩ (B ∪ C ).

Let’s make some observations:

(A0∩ B0) is everything that is both outside of A and outside of B.

(B ∪ C ) is everything in B or in C .

(A0∩ B0) ∩ (B ∪ C ) is everything in both of the above so not in A and not in B and in B or in C .

Tomasz Lechowski Maths Studies September 30, 2017 11 / 12

(28)

Mark on the diagram the set corresponding to (A0∩ B0) ∩ (B ∪ C ).

Let’s make some observations:

(A0∩ B0) is everything that is both outside of A and outside of B.

(B ∪ C ) is everything in B or in C .

(A0∩ B0) ∩ (B ∪ C ) is everything in both of the above so not in A and not in B and in B or in C .

(29)

Example 5

Mark on the diagram the set corresponding to (A0∩ B0) ∩ (B ∪ C ).

Let’s make some observations:

(A0∩ B0) is everything that is both outside of A and outside of B.

(B ∪ C ) is everything in B or in C .

(A0∩ B0) ∩ (B ∪ C ) is everything in both of the above so not in A and not in B and in B or in C .

Tomasz Lechowski Maths Studies September 30, 2017 11 / 12

(30)

Mark on the diagram the set corresponding to (A0∩ B0) ∩ (B ∪ C ).

Let’s make some observations:

(A0∩ B0) is everything that is both outside of A and outside of B.

(B ∪ C ) is everything in B or in C .

(A0∩ B0) ∩ (B ∪ C ) is everything in both of the above so not in A and not in B and in B or in C .

(31)

Example 5

Mark on the diagram the set corresponding to (A0∩ B0) ∩ (B ∪ C ).

Let’s make some observations:

(A0∩ B0) is everything that is both outside of A and outside of B.

(B ∪ C ) is everything in B or in C .

(A0∩ B0) ∩ (B ∪ C ) is everything in both of the above so not in A and not in B and in B or in C .

Tomasz Lechowski Maths Studies September 30, 2017 11 / 12

(32)

Mark on the diagram the set corresponding to (A0∩ B0) ∩ (B ∪ C ). Answer:

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