Q. 494.0( 2 Votes )

# Fill in the blanks in each of the

Let the relation R be defined on the set

A = {1, 2, 3, 4, 5} by R = {(a, b) : |a^{2} – b^{2}| < 8}. Then R is given by _______.

Answer :

Given that, A = {1, 2, 3, 4, 5} and R = {(a, b) : |a^{2} – b^{2}| < 8}

Let us check the relation for a=1,b=2

⇒ |12 – 22| = |-3|= 3 < 8

⇒ (1,2) ∈ R

Similarly, we can check for all the ordered pairs of (a,b) which satisfies the relation.

Hence, R = {(1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3),(3,4),(4,3),

(4,4),(5,5)}

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Fill in the blanks in each of the

Let the relation R be defined on the set

A = {1, 2, 3, 4, 5} by R = {(a, b) : |a^{2} – b^{2}| < 8}. Then R is given by _______.

State True or False for the statements

Every relation which is symmetric and transitive is also reflexive.

Mathematics - ExemplarState True or False for the statements

Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.

Mathematics - ExemplarState True or False for the statements

An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.

Mathematics - Exemplar