Statement 1: If a relation R on a set A satisfies R = R⁻¹, then R is symmetric. Statement 2: For a relation R to be symmetric, it is necessary that R =…

Answer: (c) Both the statements are true. R is symmetric exactly when (a,b) ∈ R ⇒ (b,a) ∈ R, i.e. R = R⁻¹; so the condition is both necessary and sufficient. Correct: (c)

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Mathematics20261 markMCQMatrices

Choose the correct option.

Statement 1: If a relation R on a set A satisfies R = R⁻¹, then R is symmetric. Statement 2: For a…

Statement 1: If a relation $R$ on a set $A$ satisfies $R = R^{-1}$, then $R$ is symmetric. Statement 2: For a relation $R$ to be symmetric, it is necessary that $R = R^{-1}$ Which one of the following is correct? (Understanding)

(a)Statement 1 is true and Statement 2 is false.
(b)Statement 2 is true and Statement 1 is false.
(c)Both the statements are true.
(d)Both the statements are false.

Answer

Official answer key

Correct option: (c)

Answer: (c) Both the statements are true. $R$ is symmetric exactly when $(a,b) \in R \Rightarrow (b,a) \in R$, i.e. $R = R^{-1}$; so the condition is both necessary and sufficient.