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IB Questionbank Mathematical Studies 3rd edition 1

1. Consider the two propositions p and q.

p: The sun is shining q: I will go swimming Write in words the compound propositions

(a) p  q;

(2)

(b) ¬p q.

(2)

The truth table for these compound propositions is given below.

p q p  q ¬p ¬p q

T T T T

T F F F

F T T T

F F T T

(c) Complete the column for ¬p.

(1)

(d) State the relationship between the compound propositions p  q and ¬p q.

(1) (Total 6 marks)

2. Two logic propositions are given

p: Dany goes to the cinema q: Dany studies for the test (a) Write in words the proposition

p  q.

(b) Given the statement s: “If Dany goes to the cinema then Dany doesn’t study for the test”.

(i) Write s in symbolic form.

(ii) Write in symbolic form the contrapositive of part (b)(i).

(Total 6 marks)

(2)

IB Questionbank Mathematical Studies 3rd edition 2

3. Consider the following statements:

p: Good mathematics students go to good universities q: Good music students are good mathematics students r: Students who go to good universities get good jobs (a) From these statements, write two valid conclusions.

(b) Write in words each of the following (i)  q;

(ii) p  r.

(Total 4 marks)

4. Three propositions are given as

p: It is snowing q: The roads are open r: We will go skiing (a) Write the following compound statement in symbolic form.

“It is snowing and the roads are not open.”

(2)

(b) Write the following compound statement in words.

(¬p  )q r

(3)

An incomplete truth table for the compound proposition (¬p  )q r is given below.

(c) Copy and complete the truth table on your answer paper.

p q r ¬p ¬p q (¬p  )q r

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

(3) (Total 8 marks)

(3)

IB Questionbank Mathematical Studies 3rd edition 3

5. Consider each of the following statements:

p: Alex is from Uruguay q: Alex is a scientist r: Alex plays the flute

(a) Write each of the following arguments in symbols:

(i) If Alex is not a scientist then he is not from Uruguay.

(ii) If Alex is a scientist, then he is either from Uruguay or plays the flute.

(3)

(b) Write the following argument in words:

 r   (q  p)

(3)

(c) Construct a truth table for the argument in part (b) using the values below for p, q, r and

 r. Test whether or not the argument is logically valid.

p q r  r

T T T F

T T F T

T F T F

T F F T

F T T F

F T F T

F F T F

F F F T

(4) (Total 10 marks)

(4)

IB Questionbank Mathematical Studies 3rd edition 4

6. Let = {x : 1 ≤ x < 17, x  }.

P , Q and R are the subsets of such that

P = {multiples of four};

Q = {factors of 36};

R = {square numbers}.

(a) List the elements of (i)

(ii) P  Q  R.

(2) (b) Describe in words the set P  Q.

(1) (c) (i) Draw a Venn diagram to show the relationship between sets P, Q and R.

(2) (ii) Write the elements of in the appropriate places on the Venn diagram.

(3) (d) Let p, q and r be the statements

p: x is a multiple of four;

q: x is a factor of 36;

r: x is a square number.

(i) Write a sentence, in words, for the statement (p  r)   q

(2) (ii) Shade the region on your Venn diagram in part (c)(i) that represents (p  r)   q

(1) (iii) (a) Use a truth table to determine the values of (p  r)   q. Write the first

three columns of your truth table in the following format.

p q r

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

(3) (b) Write down one possible value of x for which (p  r)   q is true.

(1) (Total 15 marks)

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