Let $P =$ Set of all integral multiples of $3$ ; $Q =$ Set of integral multiples of $4$ ; $R =$ Set of all integral multiples of $6$ . Consider the following relations :
$1$ $P \cup Q = R$
$2.$ $P \subset R$
$3.$ $R \subset (P \cup Q)$
Which of the relations given above is/are correct ?

only

1

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only

2

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only

3

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both

2

and

3

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Solution

The correct option is C only $3$
Given that P = ${3, 6, 9, 12, 15, 18, 21, . . .}$
Q = ${4, 8, 12, 16, 20, . . .}$
R = ${6, 12, 18, . . .}$
Considering the choices given :
1. P $\cup$ Q = ${3, 4, 6, 8, 9, 12, 16, 18, . . .}$ $\neq$ R
2. All the element of P are not in R so P $⊈$ R
3. P $\cup$ Q = ${3, 4, 6, 8, 9, 12, 15, 16, 18, . . .}$
$\Rightarrow$ All the element of R are in P $\cup$ Q
$\Rightarrow$ R $\subset$ (P $\cup$ Q)

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Similar questions

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Let P= Set of all integral multiples of 3; Q= Set of integral multiples of 4; R= Set of all integral multiples of 6. Consider the following relations :1 P∪Q=R2. P⊂R3. R⊂(P∪Q)Which of the relations given above is/are correct ?

Let $P =$ Set of all integral multiples of $3$ ; $Q =$ Set of integral multiples of $4$ ; $R =$ Set of all integral multiples of $6$ . Consider the following relations :
$1$ $P \cup Q = R$
$2.$ $P \subset R$
$3.$ $R \subset (P \cup Q)$
Which of the relations given above is/are correct ?