Representation of Sets

Interactive Feed

Consider the following statements P: Suman is brilliant Q: Suman is rich R : Suman is honest The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

\sim (Q \leftrightarrow (P \land \sim R))

\sim Q \leftrightarrow\sim P \land R

\sim (P \land \sim R) \leftrightarrow Q

\sim P \land (Q \leftrightarrow\sim R)

Let S be a non-empty subset of R. Consider the following statement : P : There is a rational number $x \in S$ such that $x > 0$ . Which of the following statements is the negation of the statement P ?

There is no rational number

x \in S

x \leq 0

Every rational number

x \in S

x \leq 0

x \in S

x \leq 0 \Rightarrow x

is not rational.

There is a rational number

x \in S

x \leq 0

JEE Main 2020 (7 January Shift 2)

Let A, B, C and D be four non-empty sets. The Contrapositive statement of “If $A \subseteq B$ and $B \subseteq D$ then $A \subseteq C$ ” is :

A \subseteq C

B \subset A

D \subset B

A \neq \subseteq C

A \subseteq B

B \subseteq D

A \neq \subseteq C

A \neq \subseteq B

B \subseteq D

A \neq \subseteq C

A \neq \subseteq B

B \neq \subseteq D

JEE Main 2025 (January)

Let $A = {1, 2, 3, \dots, 10}$ and $B = {(m, n) : m, n \in A, m < n and g cd (m, n) = 1}$ . Then $n (B)$ is equal to :