\fQuestion 3 (). Use proof by contradiction to show that "If m and no are odd integers, then m+ 71 is even." (). Prove that "x is even if and only if 3x' + 8 is even" for xeEt. ()-An integer n is called a perfect square if and only if >= ' for some integer k. Suppose that x and ) are perfect squares, prove and explain why x + )+ 2,xy is a perfect square. (v).During the MA161 lecture, the students were given an equation ax +by+c=0, where a, b and care odd integers. The students found out that the roots of the equation are not rational. Prove it? (v). In the same MA161 lecture, the students came up with an interesting observation. They found out that if you square any even integer, it ends either in 0, 4, or 6. Prove this. [3 + 5 + 5 + 5 + 3 = 21 marks] Question 4 @). Use logical equivalences, prove that An(BUC)=(AnB)(AnC).. (. Let AmBAC=AVBVC, where A, B and C are sets. a). Show that the statement holds true by showing that each side is a subset of the other side. b). Show using a membership table. Use Mathematica to verify. (mi) Find all the solutions of x x ]=x. (iv).Find all the solutions of [ x ]+ [ x ) = 2x. [4 + 3 + 3 + 3+ 3 = 16 marks]