MCQ Questions

Question No. 1

Find the truth value of P ∧ Q for each of the following pairs of statements.

Answer :

a) P: Dogs can bark. Q: 4 + 3 = 8

b) P: 23 = 6 Q: The diameter of a circle is half the length of its radius.

c) P: It is possible for a right-angled triangle to be isosceles. Q: A triangle has four sides.

d) P: 2 < 7 Q: The product of 2 and 7 is 14.

e) P: The sea is not salty. Q: A cube is a prism.

f) P: 15 is a multiple of 3. Q: −3 > −15

Question No. 2

In △Exercise 11.1 Question 1: Say whether or not each of the following are statements.

Question No. 3

Write down the letters of the statements in question 1 that are true.

Answer :

Question No. 4

Write down the letters of the statements in question 1 that are false.

Answer :

Question No. 5

Write down the letters of the statements in question 1 that might be true or false.

Answer :

Question No. 6

Copy and complete the table below by putting a tick in the correct block. The first three have been done for you.

Answer :

Question No. 7

For each of the following open statements, give possible values for the variables that will make the statement (i) true and (ii) false.

Answer :

a) 5x − 3 = 7

b) 6p = −42

c) 3a > 27

d) y = √x

e) 4x = 2x

f) y = x + 4

g) y = 3x − 11

h) x⁰ = x

Question No. 8

Write the negation of each of the following statements.

Answer :

a) My best friend’s name is Abeo.

b) Benin shares a border with Nigeria.

c) 17 − 5 ≠ 12

d) Lake Chad is completely inside Nigeria.

e) ℕ ⊂ ℚ

f) −30 ≤ −31

Question No. 9

For each of the following statements, more than one negation statement is given. Write down the numbers of each valid negation statement.

Answer :

a) P: We will go on holiday after May. ~P: (i) We will go on holiday before May. (ii) We will not go on holiday after May. (iii) It is not true that we will go on holiday after May. (iv) We will go on holiday during or before May.

b) P: Damilola and Bolaji are brothers. ~P: (i) It is not true that Damilola and Bolaji are brothers. (ii) Damilola and Bolaji are sisters. (iii) Damilola and Bolaji are not related. (iv) Damilola and Bolaji are not brothers.

c) P: Zainab is the youngest student in the class. ~P: (i) Zainab is the oldest student in the class. (ii) Zainab is not the youngest student in the class. (iii) Zainab is the second-youngest student in the class. (iv) It is not true that Zainab is the youngest student in the class. (v) Zainab is not a student in the class.

d) P: Some people enjoy horror movies. ~P: (i) Some people do not enjoy horror movies. (ii) All people enjoy horror movies. (iii) No people enjoy horror movies. (iv) All people do not enjoy horror movies.

Question No. 10

Given: P ∧ Q.

Answer :

a) What kind of compound statement is this?

b) Under what conditions is P ∧ Q true?

c) Under what conditions is P ∧ Q false?

Question No. 11

Given the following statements: P: x > y Q: xy = 20

Answer :

a) Assign any integer values between 1 and 10 to x and y in such a way that P ∧ Q is true.

b) Assign any integer values between 1 and 10 to x and y in such a way that P ∧ Q is false.

Question No. 12

Given: P ∨ Q.

Answer :

a) What kind of compound statement is this?

b) Under what conditions is P ∨ Q true?

c) Under what conditions is P ∨ Q false?

Question No. 13

Find the truth value of P ∨ Q for each of the following pairs of statements:

Answer :

a) P: Pigs can fly. Q: Water is wet.

b) P: Friday comes just before Sunday. Q: December is the shortest month of the year.

c) P: 30 ÷ 6 = 5. Q: Ice is a form of water.

d) P: There are 100 mm in 1 cm. Q: A yam is a vegetable.

e) P: 100 is a power of 10. Q: −4 > −3.

f) P: A dog can have kittens. Q: Water freezes when it boils.

Question No. 14

Given the following statements: P: x > y; Q: x + y = 11

Answer :

a) Assign any integer values between 1 and 10 to x and y in such a way that P ∨ Q is true.

b) Assign any integer values between 1 and 10 to x and y in such a way that P ∨ Q is false.

Question No. 15

Given: P ⇒ Q.

Answer :

a) What kind of compound statement is this?

b) Under what conditions is P ⇒ Q true?

c) Under what conditions is P ⇒ Q false?

Question No. 16

In the statement ‘If she saves her money, she will be able to buy a new bicycle’, write down the:

Answer :

a) antecedent

b) consequent

Question No. 17

Find the truth value of P ⇒ Q for each of the following pairs of statements:

Answer :

a) P: 81 is a power of 3. Q: 3 is a factor of 81.

b) P: 3 is a factor of 24. Q: 24 is a power of 3.

c) P: ₦1 = 100 Kobo. Q: 300 Kobo is worth ₦3.

d) P: 5 ≤ 3. Q: The product of 8 and 3 is 24.

e) P: 8 < 7. Q: The sum of 7 and 8 is 51.

f) P: The earth has a magnetic North pole. Q: North is opposite East.

Question No. 18

Given: P ⇔ Q.

Answer :

a) What kind of compound statement is this?

b) Under what conditions is P ⇔ Q true?

c) Under what conditions is P ⇔ Q false?

Question No. 19

Find the truth value of P ⇔ Q for each of the following pairs of statements.

Answer :

a) P: The Sun rises in the East. Q: The Sun sets in the West.

b) P: Hausa is spoken in Nigeria. Q: Yoruba is not spoken in Nigeria.

c) P: 5 is a factor of 20. Q: 20 is a multiple of 5.

d) P: April is the first month of the year. Q: March is the last month of the year.

e) P: 2 + 2 = 5. Q: 5 + 5 = 10.

f) P: A is the first letter of the alphabet. Q: All first names begin with an A.

Question No. 20

What does each of the following symbols mean?

Answer :

a) ~

b) ∧

c) ∨

d) ⇒

e) ⇔

Question No. 21

Draw up a truth table for P and ~P. (Hint: Your table will have only two columns: one for P and one for ~P.)

Answer :

Question No. 22

Given the statements P: ‘it is cold’ and Q: ‘the wind is blowing’, 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. 23

Given the statements P: ‘she is kind’ and Q: ‘she is clever’, write each of the following in logical notation, using P and Q.

Question No. 24

Find the truth value of each of the following compound statements.

Answer :

a) If 3 + 2 = 7, then 7 + 2 = 9.

b) 8 + 8 = 10 if and only if 4 + 4 = 5.

c) 1 + 1 = 3 or 1 + 2 = 3.

d) 6 − 1 = 5 and 5 − 6 = 1.

e) If 1 < 4, then −1 < −4.

Chapter

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