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Q2 (5 marks) Let $X={0,2,4,6,…,200}$ (i.e., $X$ contains all multiples of 2 between 0 and 200 inclusive) ane suppose $A?X$ with $?A??53$. Show there must exist distinct $a,b?A$ satisfying the following tw properties simultaneously: (i) $a+b$ is divisible by 51 , and (ii) $a?b$ is divisible by 4 .

Here is your answer-We can prove this by contradiction. Suppose that there do not exist distinct elements a,b in A such that a+b is divisible by 51 an

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