MCQ Questions

Question No. 1

For each of the statements below, say whether it is open or closed. For each closed statement, say whether it is true or false.

Answer :

a) No even integers are divisible by 3.

b) 13 − 5 = 8

c) Next Wednesday is a public holiday.

d) Some integers are negative.

e) 17 and 18 are consecutive numbers.

f) x > 45

g) All integers are natural numbers.

h) Some children are not fond of vegetables.

Question No. 2

Given the statements P: x > y and Q: xy = 24, assign any integer values between 1 and 10 to x and y in such a way that:

Answer :

a) P ∧ Q is true

b) P ∧ Q is false

c) P ∨ Q is true

d) P ∨ Q is false

Question No. 3

Given the statements P: ‘It is raining’ and Q: ‘The roof is leaking’, write down a simple sentence that describes each of the following logical statements.

Answer :

a) ~P

b) ~Q

c) P ∧ Q

d) P ∨ Q

e) ~~Q

f) P ⇒ Q

g) Q ⇔ P

h) P ⇒ ~Q

Question No. 4

Construct a truth table to show that (P ∨ Q) ⇒ (~Q ⇒ P) is a tautology.

Answer :

Question No. 5

Construct a truth table for each of these compound statements.

Answer :

a) ~P ∨ Q

b) ~P ∧ ~Q

c) P ∨ (P ⇒ Q)

d) (~P ∧ Q) ∨ ~Q

Question No. 6

If a shape is a square, then it is a quadrilateral.

Answer :

a) Write the statement in logical notation. Is the statement true or false?

b) Write the converse statement in logical notation and in words. Is the converse statement true or false? Give a reason for your answer.

c) Write the inverse statement in logical notation and in words. Is the inverse statement true or false? Give a reason for your answer.

d) Write the contrapositive statement in logical notation and in words. Is the contrapositive statement true or false? Give a reason for your answer.

Question No. 7

If a polygon has three sides, then it is a triangle.

Answer :

a) Write the statement in logical notation. Is the statement true or false?

b) Write the converse statement in logical notation and in words. Is the converse statement true or false? Give a reason for your answer.

c) Write the inverse statement in logical notation and in words. Is the inverse statement true or false? Give a reason for your answer.

d) Write the contrapositive statement in logical notation and in words. Is the contrapositive statement true or false? Give a reason for your answer.

Question No. 8

If x is a factor of 6, then x is a factor of 12.

Answer :

a) Write the statement in logical notation. Is the statement true or false?

b) Write the converse statement in logical notation and in words. Is the converse statement true or false? Give a reason for your answer.

c) Write the inverse statement in logical notation and in words. Is the inverse statement true or false? Give a reason for your answer.

d) Write the contrapositive statement in logical notation and in words. Is the contrapositive statement true or false? Give a reason for your answer.

Question No. 9

If x is an even prime number, then x is 2.

Answer :

a) Write the statement in logical notation. Is the statement true or false?

b) Write the converse statement in logical notation and in words. Is the converse statement true or false? Give a reason for your answer.

c) Write the inverse statement in logical notation and in words. Is the inverse statement true or false? Give a reason for your answer.

d) Write the contrapositive statement in logical notation and in words. Is the contrapositive statement true or false? Give a reason for your answer.

Question No. 10

Construct a truth table for each of the following.

Answer :

a) P ⇒ Q

b) Q ⇒ P

c) ~P ⇒ ~Q

d) ~Q ⇒ ~P

Question No. 11

What do you notice about your answers to a) and d) in question 1?

Answer :

Question No. 12

What do you notice about your answers to b) and c) in question 1?

Answer :

Question No. 13

Use truth tables to decide whether or not each of the following pairs of statements are equivalent.

Answer :

a) ~(P ∧ Q) and ~P ∧ ~Q

b) ~(P ∧ Q) and ~P ∨ ~Q

c) ~(P ∨ Q) and ~P ∨ ~Q

d) ~(P ∨ Q) and ~P ∧ ~Q

Question No. 14

Solve: Use an indirect proof (either method) to prove each of the following.

Answer :

a) The sum of two odd numbers is always an even number.

b) A triangle can have at most one right angle.

c) Every angle in an equilateral triangle is equal to 60°

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