MTH202 Practice Questions Lectures 1-45 Set 2

Solution File Lecture No 1-3

Q1. Let p be “I am intelligent” and let q be “I have a book”, Give a simple verbal sentence which

describes each of the following statement:

(a) p

(b) p q

(c) q p

Solution:

(a) I am not intelligent

(b) I am intelligent or I have a book

(c) I have a book but I am not intelligent

Q2. Construct a truth table for the compound proposition

p p q q

Solution: · p · q · ~p · ~p →q · P^(~p→q)

p p q q

T T F T T T

T F F T T F

F T T T F T

F F T F F T

Q3. Convert into logical form and then write converse, inverse and contra positive of the following

statement.

“If I study, then I shall pass the test”.

Solution:

Inverse: If I do not study, then I shall not pass the test.

Converse: If I shall pass the test then Istudy.

Contrapositive: if I shall not pass the test then I do not study.

Q4. Let p = “Ahmad eats apple”, q = “Ahmad eats banana” and r = “Ahmad eats grapes”. Write each

of the following in symbolic form:

a) Ahmad eats apple or banana but not grapes.

b) It is not true that Ahmad eats apple but not grapes.

c) It is not true that Ahmad eats apples or bananas but not grapes.

Solution:

i) p q r

ii) p r

iii) ~ ( p q r

Q5. Assume that for the truth values p = F and q = T. Show that the proposition

p q p p q is true.

Solution:

p q ~p ~q (p q) (p ~ q) ~ p (p ~ q) p q p p q

F T T F F F T T

Hence the given proposition is true.

Q6. Use truth table to verify the statement (how to prove it using laws)

q (p q) q p q

Solution: · p · q

(p q) q p q (p q) q (p q)

T T T T T T

T F F F F F

F T F T T T

F F F F T F

Therefore from column 4&6, q (p q) q p q

Q7. Question No 8:

Use De Morgan’s laws to find the negation of

“Ahmad loves football and his brother loves cricket”

Solution:

Let p=Ahmed loves football

q=His brother loves cricket

p q = Ahmed loves football and His brother loves cricket

Using De Morgan’s law

p q p q =Ahmed does not love football or his brother does not love cricket