isi-entrance 2012 Q28

isi-entrance · India · solved Inequalities Set Operations Using Inequality-Defined Sets

Let $A = \{(x,y) : x^4 + y^2 \leq 1\}$ and $B = \{(x,y) : x^6 + y^4 \leq 1\}$. Which of the following is true?
(A) $A = B$
(B) $A \subset B$ (A is a proper subset of B)
(C) $B \subset A$ (B is a proper subset of A)
(D) Neither $A \subset B$ nor $B \subset A$

$x^6 + y^4 - (x^4 + y^2) = x^4(x^2-1) + y^2(y^2-1) \leq 0$ when $x^4 + y^2 \leq 1$. So $A \subseteq B$. (B)

Let $A = \{(x,y) : x^4 + y^2 \leq 1\}$ and $B = \{(x,y) : x^6 + y^4 \leq 1\}$. Which of the following is true?

(A) $A = B$

(B) $A \subset B$ (A is a proper subset of B)

(C) $B \subset A$ (B is a proper subset of A)

(D) Neither $A \subset B$ nor $B \subset A$

Paper Questions

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