JEE MATHEMATICS MCQ: SET THEORY

1 Easy

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Analyzing +4 | -1

Let R1, R2 are relations defined on Z such that a

a{R_1}b \Leftrightarrow (a - b)

is divisible by 3 and a R2

b \Leftrightarrow (a - b)

is divisible by 4. Then which of the two relations

\left( {{R_1} \cup {R_2}} \right),\left( {{R_1} \cap {R_2}} \right)

is an
equivalence relation?

View answer and explanation

Correct option: B

\left(R_1 \cap R_2\right)

only

Option B (

\left(R_1 \cap R_2\right)

only) is correct because the intersection of equivalence relations is always an equivalence relation, while the union is not necessarily so.

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2 a_1 a_2 a_3 \ldots . . a_{2006}

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n

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C

2 \%

A