Write out the set of ordered pairs in the following relations on the integers (x

Question

Write out the set of ordered pairs in the following

relations on the integers

(x,y) is in the relation is and only if x < 2y

(x,y) is in the relation is and only if 3x-y=2

(x,y) is in the relation is and only if xy=3

(x times y equals 3)

(x,y) is in the relation is and only if 4x=y

Explanation / Answer

(x,y) is in the relation is and only if x < 2y. The set is { ( 2x,x+z)|x Z, z > 0 Z}. (x,y) is in the relation is and only if 3x-y=2. The set is { (x,3x-2) |x Z}. 3.(x,y) is in the relation if and only if xy=3 . The set is {(x,3/x)| x Z and x is a divisor of 3}. (x times y equals 3) is same as xy = 3. The set is {(x,3/x)| x Z and x is a divisor of 3}. (x,y) is in the relation is and only if 4x=y. The set is {(x,4x)| x Z}.

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