MAD101_Final test

Which of the following option is true?

• If the Sun is a planet, elephants will fly

• 3 +2 = 8 if 5+2 = 7

• 1 > 3 and 3 is a positive integer

• -2 > 3 or 3 is a negative integer

Answer explanation

Explanation: Hypothesis is false, thus the whole statement is true.

What is the value of x after this statement, assuming the initial value of x is 5?

‘If x equals to one then x=x+2 else x=0’.

• 1

• 3

• 0

• 2

Answer explanation

If condition is false so value decided according to else condition.

Let P: If Sahil bowls, Saurabh hits a century.; Q: If Raju bowls, Sahil gets out on first ball. Now if P is true and Q is false then which of the following can be true?

• Raju bowled and Sahil got out on first ball

• Raju did not bowled

• Sahil bowled and Saurabh hits a century

• Sahil bowled and Saurabh got out

Answer explanation

Either hypothesis should be false or both (hypothesis and conclusion) should be true.

p → q is logically equivalent to ​ (a)   .

• ¬p ∨ q
• ¬p ∨ ¬q
• p ∨ ¬q
• ¬p ∧ q
• : (p → q) ↔ (¬p ∨ q) is tautology.

Answer explanation

(p → q) ↔ (¬p ∨ q) is tautology.

¬ (p ↔ q) is logically equivalent to ​ (a)   .

• p↔¬q
• q↔p
• ¬p↔¬q
• ¬q↔¬p

Answer explanation

¬(p↔q)↔(p↔¬q) is tautology.

p ∧ q is logically equivalent to ​ (a)   .

• ¬ (p → ¬q)
• (p → ¬q)
• (¬p → ¬q)
• (¬p → q)

Answer explanation

(p ∧ q) ↔ (¬(p → ¬q)) is tautology.

Which of the following statement is correct?

• p ∨ q ≡ q ∨ p

• ¬(p ∧ q) ≡ ¬p ∨ ¬q

• (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

• All of mentioned

Answer explanation

Verify using truth table, all are correct.

. p ↔ q is logically equivalent to ________.

• (p → q) → (q → p)

• (p → q) ∨ (q → p)

• (p → q) ∧ (q → p)

• (p ∧ q) → (q ∧ p)

Answer explanation

(p ↔ q) ↔ ((p → q) ∧ (q → p)) is tautology.

(p → q) ∧ (p → r) is logically equivalent to ________

• p → (q ∧ r)

• p → (q ∨ r)

• p ∧ (q ∨ r)

• p ∨ (q ∧ r)

Answer explanation

((p → q) ∧ (p → r)) ↔ (p → (q ∧ r)) is tautology.

The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.

• ∃x(C(x) ∧ F (x))

• ∀x(C(x) ∧ F (x))

• ∃x(C(x) → F (x))

• ∀x(C(x) → F (x))

Answer explanation

For every person x, if comedian then x is funny.