Let A and B be two sets defined as A - x-x - and -1-2x-35- 3 and B- x - x - and 0 -3-x7- 1- If P - A-B and Q - B-A- then the value of nP- Q is

A = {x : x ∈𝕎 and 1≤2x+35≤ 3} 1≤2x+35≤ 3 ⇒ 5 ≤ 2x+3 ≤ 15 ⇒ 8 ≤ 2x≤ 12 ⇒ 4 ≤ x≤ 6 As x∈𝕎, so we get nbsp; A ={0, 1, 2, 3, 4, 5, 6} B= {x: x ∈ℤ and 0 ≤3 ...

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Byju's Answer

Standard XII

Mathematics

Properties of Composite Function

Let A and B b...

Question

Let $A$ and $B$ be two sets defined as $A = {x : x \in W and - 1 \leq \frac{2 x + 3}{5} \leq 3}$ and $B = {x : x \in Z and 0 \leq \frac{3 - x}{7} \leq 1}$ . If $P = A - B$ and $Q = B - A$ , then the value of $n (P \times Q)$ is

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Solution

The correct option is C $12$
$A = {x : x \in W and - 1 \leq \frac{2 x + 3}{5} \leq 3}$
$- 1 \leq \frac{2 x + 3}{5} \leq 3 \Rightarrow - 5 \leq 2 x + 3 \leq 15 \Rightarrow - 8 \leq 2 x \leq 12 \Rightarrow - 4 \leq x \leq 6$
As $x \in W$ , so we get
$A = {0, 1, 2, 3, 4, 5, 6}$

$B = {x : x \in Z and 0 \leq \frac{3 - x}{7} \leq 1}$
$0 \leq \frac{3 - x}{7} \leq 1 \Rightarrow 0 \leq 3 - x \leq 7 \Rightarrow - 3 \leq - x \leq 4 \Rightarrow - 4 \leq x \leq 3$
As $x \in Z$ , so we get
$B = {- 4, - 3, - 2, - 1, 0, 1, 2, 3}$

Now, $P = A - B = {4, 5, 6}$
and $Q = B - A = {- 4, - 3, - 2, - 1}$
$n (P \times Q) = n (P) \times n (Q) = 3 \times 4 = 12$

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Similar questions

Q. Let

A

and

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be two sets defined as

A = {x : x \in W and - 1 \leq \frac{2 x + 3}{5} \leq 3}

and

B = {x : x \in Z and 0 \leq \frac{3 - x}{7} \leq 1}

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Let A and B be two sets defined as A={x:x∈W and −1≤2x+35≤3} and B={x:x∈Z and 0≤3−x7≤1}. If P=A−B and Q=B−A, then the value of n(P×Q) is

Let $A$ and $B$ be two sets defined as $A = {x : x \in W and - 1 \leq \frac{2 x + 3}{5} \leq 3}$ and $B = {x : x \in Z and 0 \leq \frac{3 - x}{7} \leq 1}$ . If $P = A - B$ and $Q = B - A$ , then the value of $n (P \times Q)$ is