The relation defined on the power set $P (A)$ of a set $A$ such that $(X, Y) \in R \Rightarrow X \subseteq Y$ is

symmetric

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anti-symmetric

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equivalence realtion

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none

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Solution

The correct option is A anti-symmetric
Relation on the power set $P (A)$ of a set $A$ such that $(X, Y) \in R \Rightarrow X \subseteq Y$
if $X \subseteq Y$ and $Y \subseteq X$ then $X = Y$
A relation $R$ is said to be anti-symmetric iff $a R b$ and $b R a$ $\Rightarrow a = b$
Therefore, given relation is anti-symmetric.

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Similar questions

Write the following relations as the sets of ordered pairs :

(i) A relation R from the set {2, 3, 4, 5, 6} to the set {1, 2, 3} defined by x = 2y.

(ii) A relation R from the set {1, 2, 3, 4, 5, 6, 7} defined by $(x, y) ϵ R \Leftrightarrow x$ is relatively prime to y.

(iii) A relation R on the set {0, 1, 2, ...., 10} defined by 2x + 3y = 12.

(iv) A relation R from a set A = {5, 6, 7, 8} to the set B = {10, 12, 15, 16, 18} defined by $(x, y) ϵ R \Leftrightarrow x$ divides y.

A = {x : 1 < | x | \leq 4, x \in Z}

R = {(x, y) : y = | x |} .

R

A = [x :∣ x ∣< 3, x ϵ Z]

Z

R = [(x, y) : y =∣ x ∣, x \neq - 1]

R

ϵ

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