Mock Test 1 — Mathematical Reasoning

The negation of "If $n$ is a prime number, then $n$ is odd or $n = 2$" is:

Which of the following is the contrapositive of "If two triangles are congruent, then their areas are equal"?

The compound statement $(p \wedge q) \Rightarrow (p \vee q)$ is:

The negation of "$\forall x \in \mathbb{R}, \exists y \in \mathbb{R}, y > x$" is:

Let $p$: "Suman is brilliant" and $q$: "Suman is rich". The compound statement "Suman is neither brilliant nor rich" is:

If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p, q, r$ are respectively:

The converse of "If $x$ is an even integer, then $x + 2$ is an even integer" is:

Which of the following is a tautology?

The statement $\sim(p \Leftrightarrow \sim q)$ is logically equivalent to:

The negation of the statement "If $x$ is real, then $x^2 \geq 0$" is:

How many distinct truth value combinations are there in the truth table of a compound statement involving exactly 3 atomic statements $p, q, r$? (Give the integer value.)

Consider the compound statement $(p \Rightarrow q) \wedge (q \Rightarrow r) \Rightarrow (p \Rightarrow r)$. The number of rows in the truth table where this compound statement is TRUE is (out of 8 rows total).

For how many truth value assignments to $(p, q)$ is the statement $p \Leftrightarrow q$ true (out of the 4 possible assignments)?

Assertion (A): The contrapositive of "If $x$ is a multiple of 6, then $x$ is a multiple of 2" is logically equivalent to the original statement.
Reason (R): For any conditional statement $p \Rightarrow q$, the contrapositive $\sim q \Rightarrow \sim p$ is logically equivalent to it.

Assertion (A): The statement $p \vee \sim p$ is always true regardless of the truth value of $p$.
Reason (R): This is known as the Law of Excluded Middle, a fundamental tautology in classical logic.