1. The set of values of x satisfying 26 = 5 (mod x) is a. {3,7} b. {1,3,7} c. {3,2,1} d. {3,7,21} 2. The set of value of x satisfying 3x = 2 (mod5) is a. 1 b. 2 c. 3 d. 4 3. Which of the following relations on {0,1,2,3} is an equivalence relation. a. {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)} b. {(0,0), (1,1), (2,2), (3,3)} c. {(0,0), (0,1), (0,2), (1,0), (1,1), (12), (2,0)} d. {(0,0), (0,2), (2,3), (1,1), (2,2)}

Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?

Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.

In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.