y ∈ Z} and B = {x ∈ Z : x = 2z for some z ∈ Z}. Then
(i) A and B are equal,
(ii) A {\displaystyle \subsetneq } B,
(iii) B {\displaystyle \subsetneq } A
(1) (i) only
(2) (ii) only.
(3) (iii) only
(4) None of the given answers is true.
Q2.
Consider a function f: R → R^+ defined as f(x) =e^x: Then the image of S ={x ∈ R: 0 ≤ x^2 - 9} is
(i) (-∞; e^-3]U[e^3;∞);
(ii) [e^-3; e3^];
(iii)[e^3;∞)
(4) None of the given answers is true.
Q3.
The two distinct square roots of i is
(1) √2 + √2i and -√2 - √2i
(2) 2√2 + 2√2i and - 2√2 - 2√2i
(3)√2/2 + √2/2(I) and - √2/2 - √2/2(I)
(4) None of the given answers is true.
1
Expert's answer
2022-01-18T13:09:13-0500
Q1.A={x∈Z:x=2(y−2),y∈Z}B={x∈Z:x=2y,y∈Z}If, k∈A then k=2(k′−2) for some k′∈Zk′∈Z⇒k′′=k′−2∈ZNow, k=2k′′,k′′∈Z⇒k∈B⇒A⊆BSimillarly,If, l∈B then l=2l′ for some l′∈Zl′∈Z⇒l′′=l′+2∈ZNow, l=2(l′′−2),l′′∈Z⇒l∈A⇒B⊆AHence, A=B
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