If $x$ and $y$ are both positive, $x$ is even, and $y$ is odd, select the one of the following that must be odd.

x y

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x + 2 y

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x^{y}

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y^{x}

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\frac{x}{y}

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Solution

The correct option is D $y^{x}$
$x$ is even, $y$ is odd.
$x y$ = even $\times$ odd = even
$x + 2 y$ = even+even=even
$x^{y}$ = even raised to odd = even
$y^{x}$ = odd raised to even = odd
$\frac{x}{y}$ = can not be said whether even or odd
so D is correct option.

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Similar questions

Prove that the following statement is true : If x, $y \in Z$ such that x and y are odd, then xy is odd.

Check whether the following ststement are true or not :

(i) p : If x and y are odd integers, then x + y is an even integer.

(ii) q : If x, y are integers such that xy is even, then at least one of x and y is an even integer.

Find the truth value of the following statement : "If x, y $\in Z$ are such that x and y are odd, then xy is odd."

x^{y} = y^{x}

x^{2} = y,

x

y

x + 2 y

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