Question

If A = {-1, 0, 1, 2, 3}, write the subset S of A × A such that
the second component of the elements of S is 0.

Answer 1

To find:

the subsets S of Set A×A such that the second component of all the elements of S is 0 .

Given :

A = {-1,0,1,2,3}

Solution :

A×A ={{-1,0},{0,0},{1,0},{2,0},{3,0},{-1,-1},{-1,1},{-1,2},{-1,3},{0,-1},{0,1},{0,2},{0,3},{1,-1},{1,1},{1,2},{1,3},{2,-1},{2,1},{2,2},{2,3},{3,-1},{3,1},{3,2},{3,3}}

so, all the elements with second component 0 :

{-1,0},{0,0},{1,0},{2,0},{3,0}

so, S = {-1,0},{0,0},{1,0},{2,0},{3,0}