Which of these relation on the set of all people are equivalence relation ? Determine the properties of an equivalence relation that the other lack.

 

(1) {(a,b) | a and b are the same age}

(2) {(a,b) | a and b have the same parents}

(3) {(a,b) | a and b share a common parents}

(4) {(a,b) | a and b have met}

(5) {(a,b) | a and b speak common language}

 

Appreciate your reply.

Draw up table with three columns, one for each of the properties of an equivalence relation and a row for each of the given relations, work though it systematically, ticking each property fulfilled and crossing each one not fulfilled.