PLEASE DO NOT COPY OTHERS ANSWER, THANK YOU! Let x1, x2, · · · , xn...

PLEASE DO NOT COPY OTHERS ANSWER, THANK YOU!

Let x1, x2, · · · , xn ∈ {0, 1}.

(a) (10 points) Consider the equation x1 + x2 + · · · + xn = 0 mod 2. How many solutions does this equation have? Express your answer in terms of n. For example, if n = 2, x1 + x2 = 0 has 2 solutions: (x1, x2) = (0, 0) and (x1, x2) = (1, 1).

(b) (5 points) Consider the equations x1 + x2 + · · · + xn = 0 mod 2 x1 + x2 + · · · + x10 = 0 mod 2 for n ≥ 10. How many solutions are there satisfying both equations?

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orchestra answered 1 year ago

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