In the previous question, if only b = 0 and a is nonzero, the LHS becomes odd. Say True or False.

[The equation is $2^{a} + 3^{b}$ = 4 and a, b are whole numbers]

True

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False

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Solution

The correct option is A
True

If b = 0, $2^{a} + 3^{b} = 2^{a} + 1$ .

This would be even ONLY if a is also 0. If a takes any whole number other than 0, $2^{a} + 1$ would be odd as $2^{a}$ is even and 1 is odd, a summation of an even and odd gives an odd number.

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