2. [2 marks]. Prove or disprove the equality x + (y (B 2) = (x + y) (B (x + z) for the Boolean variables x. y, and z. 3. [3 marks]. Suppose that there are 5 members on a committee. Albert and Billy. for their own petty reasons. always vote the opposite of Charlie. Danielle and Evo vote how they please. Design a circuit that implements majority voting of this committee. 4. [6 marks]. Let R be the relation on integers which relates the integer x to the integer y precisely when x y is a multiple of 3. (a) Give 2 examples of integers x that are related to 4. (b) Prove that the relation R is an equivalence relation. (c) We denote the equivalence classes [0]. [1] and [2] of this equivalence relation simply by the symbols 0, l, and 2. Prove that 1 + 2 is well dened (in the sense that it is not ambiguous) and is equal to 0. [Note: what is meant by 1 + 2 is any element of the equivalence class 1 added to any element of the equivalence class 2.]