Discrete Mathem...

What is logically equivalent to the following statement?” I pass only if you pass”

(Note that fail is equivalent to not pass.)

Match the following rules of inference with its corresponding name.

Which of the following is/are equivalent to [(p V q) ∧ ¬ p → ¬ q]?

A logical binary relation $, is defined as follows:

Let ~ be the unary negation NOT operator, with higher precedence that $. Which of the following is equivalent to X V Y?

Consider the statement

Not all good-looking people are nice.

P(x): good-looking people

N(x): Nice

Which one of the following logical formula represents the above statement?

If T(x) denotes is a trigonometric function, P(x) denotes x is a periodic function and C(x) denotes x is a continuous function then the statement “It is not the case that some trigonometric functions are not periodic” can be logically represented as

Which of the following is true?

I. ¬ (P ↔ Q) ≡ P ↔ ¬ Q

II. (P ↔ Q) ≡ (P ∧ Q) ∨ (¬ P ∧ ¬ Q)

Consider the following statements:

P: Good mobile phones are not cheap

Q: Cheap mobile phones are not good

Which one of the following is/are CORRECT?

Consider the statements below:

“There is a country that borders both India and Nepal.”

If X ≡ A → ¬ B, Y ≡ ¬ B → ¬ C, Z ≡ A→ ¬ C then (X ∧ Y) → Z is

I. Valid