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Question

Let S1,S2,S3 and S4 be four sets defined as
S1={x:xZ and log2|43x|2}
S2={x:xZ and 1|x|1+|x|13}
S3={x:x23x+2 sgn(x)=0}, where sgn(x) represents the signum function.
S4={(x,y):x,yZ, x2+y24}.

List I has four entries and List II has five entries. Each entry of List I is to be correctly matched with a unique entry of List II.

List IList II (A)n(S1ΔS2)(P)9(B)n((S1×S2)(S2×S1))(Q)12(C)n(S1S2S3)(R)36(D)n(S4×S3)(S)2(T)0

Which of the following is the only CORRECT combination?

A
(A)(T)
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B
(A)(P)
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C
(B)(P)
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D
(B)(Q)
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Solution

The correct option is C (B)(P)
For S1:
log2|43x|2
|43x|22 and 43x0
443x4 and 3x4
83x0 and 3x4
83x0 and 3x4
Since xZ,
we have S1={0,1,2}

For S2:
1|x|1+|x|13
11+|x|13
11+|x|13

1+|x|3
|x|2x[2,2]
Since xZ,
we have S2={2,1,0,1,2}

S1ΔS2=(S1S2)(S1S2)
={2,1}
n(S1ΔS2)=2

n((S1×S2)(S2×S1))=(n(S1S2))2=9

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