SA

Let $n$ be a fixed positive integer. Define a relation $R$ in $Z$ as follows $\forall a, b \in Z$, $a R b$ if and only if $a - b$ is divisible by $n$. Show that $R$ is an equivalence relation.

SA

Let $A = \{1, 2, 3\}$. Then, find the number of relations containing $(1, 2)$ and $(1, 3)$, which are reflexive and symmetric but not transitive.

VSA

Let $f : R \to R$ be defined as $f(x) = \frac{x^2 + 1}{2}$, then check whether $f$ is one-one or onto.

LA

Check whether the relation S in the set of real numbers R defined by $S=\{(a,b)$: where $a-b+\sqrt{2}$ is an irrational number is reflexive, symmetric or transitive.

LA

Show that the relation $S$ on the set $A = \{x \in Z : 0 \le x \le 12\}$ given by $S = \{(a, b) : a, b \in Z, |a - b| \text{ is divisible by } 3\}$ is an equivalence relation. [All India 2019]

View All Questions