Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Let A = {0, 1, 2, 3} and define a relation R on A as follows: R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}. Is R reflexive? symmetric? transitive?

In the set of natural numbers N, define a relation R as follows: ∀ n, m ∈ N, nRm if on division by 5 each of the integers n and m leaves the remainder less than 5, i.e. one of the numbers 0, 1, 2, 3 and 4. Show that R is equivalence relation. Also, obtain the pairwise disjoint subsets determined by R

Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is ______.

Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and only if l is perpendicular to m ∀ l, m ∈ L. Then R is ______.

For real numbers x and y, define xRy if and only if x – y + `sqrt(2)` is an irrational number. Then the relation R is ______.

Consider the set A = {1, 2, 3} and R be the smallest equivalence relation on A, then R = ______

Let Z be the set of integers and R be the relation defined in Z such that aRb if a – b is divisible by 3. Then R partitions the set Z into ______ pairwise disjoint subsets

Consider the set A = {1, 2, 3} and the relation R = {(1, 2), (1, 3)}. R is a transitive relation.

Let A = {a, b, c} and the relation R be defined on A as follows:
R = {(a, a), (b, c), (a, b)}.
Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive

Let n be a fixed positive integer. Define a relation R in Z as follows: ∀ a, b ∈ Z, aRb if and only if a – b is divisible by n. Show that R is an equivalance relation

If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, transitive but not symmetric

If A = {1, 2, 3, 4 }, define relations on A which have properties of being: 
symmetric but neither reflexive nor transitive

If A = {1, 2, 3, 4 }, define relations on A which have properties of being: 
reflexive, symmetric and transitive

Let R be relation defined on the set of natural number N as follows:
R = {(x, y): x ∈N, y ∈N, 2x + y = 41}. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive

Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
an injective mapping from A to B

Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from A to B which is not injective

Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from B to A

Give an example of a map which is one-one but not onto

Give an example of a map which is not one-one but onto

Give an example of a map which is neither one-one nor onto