If A- x -x -2 - y - y - 2- x- y- and B - y - x-3 - y- x - 3- x- y- then

If nbsp; y lt; 2 nbsp; ⇒ nbsp; y = {0, 1} x 2 = y ⇒ nbsp; x 2 = 0 ⇒ x = 2 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Byju's Answer

Standard XIII

Mathematics

Cartesian Product

If A= x :x -2...

Question

If $A = {x : x - 2 = y, y < 2, x, y \in W}$ and $B = {y : x + 3 = y, x < 3, x, y \in W},$ then

A = {2, 3}

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B = {3, 4, 5}

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(A - B) \cap (B - A) = ϕ

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n ((A Δ B) \times (B Δ A)) = 9

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Solution

The correct option is D $n ((A Δ B) \times (B Δ A)) = 9$
If $y < 2 \Rightarrow y = {0, 1}$
$x - 2 = y \Rightarrow x - 2 = 0 \Rightarrow x = 2$
$x - 2 = 1 \Rightarrow x = 3$
$A = {2, 3}$

Now, $x < 3 \Rightarrow x = {0, 1, 2}$
$x + 3 = y \Rightarrow 0 + 3 = y \Rightarrow y = 3$
$1 + 3 = y \Rightarrow y = 4$
$2 + 3 = y \Rightarrow y = 5$
$∴ B = {3, 4, 5}$

Now, $A - B = {2}, B - A = {4, 5}$
$(A - B) \cap (B - A) = ϕ$
$A Δ B = (A - B) \cup (B - A)$
$= {2, 4, 5}$
$n ((A Δ B) \times (B Δ A)) = 3^{2} = 9$

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If A={x:x−2=y,y<2,x,y∈W} and B={y:x+3=y,x<3,x,y∈W}, then

The correct option is D n((AΔB)×(BΔA))=9If y<2⇒y={0,1} x−2=y⇒x−2=0⇒x=2 x−2=1⇒x=3 A={2,3} Now, x<3⇒x={0,1,2} x+3=y⇒0+3=y⇒y=3 1+3=y⇒y=4 2+3=y⇒y=5 ∴B={3,4,5} Now, A−B={2},B−A={4,5} (A−B)∩(B−A)=ϕ AΔB=(A−B)∪(B−A) ={2,4,5} n((AΔB)×(BΔA))=32=9

If $A = {x : x - 2 = y, y < 2, x, y \in W}$ and $B = {y : x + 3 = y, x < 3, x, y \in W},$ then