Let $N$ be the set of natural numbers and for $a \in N, a N$ denotes the set $\{a x: x \in N\}.$ If $b N \cap c N=d N,$ where $b, c, d$ are natural numbers greater than 1 and the greatest common divisor (GCD) of $b$ and $c$ is 1, then $d$ equals

JEE MATHEMATICS MCQ: SET THEORY

1 Easy

1 of 1

Analyzing +4 | -1

Let

N

be the set of natural numbers and for

a \in N, a N

denotes the set

\{a x: x \in N\}.

b N \cap c N=d N,

where

b, c, d

are natural numbers greater than 1 and the greatest common divisor (GCD) of

b

and

c

is 1, then

d

equals

View answer and explanation

Correct option: D

bc

The correct answer is D (

bc

). Since GCD(b, c) = 1, the least common multiple is bc, and bN ∩ cN represents multiples of both b and c, hence multiples of bc.

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S

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

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

S

a N=\{a n: n \in N: b N=\{n b: n \in N\}

c N=\{c N: n \in N\}

b N \cap c N=d N

a, b, c \in N

b, c

A=\{x: x

\}

B=\{x: x

A-B

F(n)

n

[\mathrm{F}(20) \cap \mathrm{F}(16)] \subseteq \mathrm{F}(\mathrm{y})

40 \%

A, 20 \%

10 \%

C

A

C

4 \%

A

C

2 \%

A