2. (9 points) For each of the following relations either prove that it is an equivalence relation or show why it is not. (a) For people r and y in the set of all people, R = {x,y|x and y speak a common language}. Solution: Type your solution here. (b) For people x and y in the set of all people, R = {x,ylx and y share a common parent}. Solution: Type your solution here. (c) For ordered pairs of positive integers (a, b), (c,d), R = {(a,b), (c,d)|a +d=b+c}. Solution: Type your solution here. 2. (9 points) For each of the following relations either prove that it is an equivalence relation or show why it is not. (a) For people r and y in the set of all people, R = {x,y|x and y speak a common language}. Solution: Type your solution here. (b) For people x and y in the set of all people, R = {x,ylx and y share a common parent}. Solution: Type your solution here. (c) For ordered pairs of positive integers (a, b), (c,d), R = {(a,b), (c,d)|a +d=b+c}. Solution: Type your solution here