Given two sets:
A={x∣−3<x<8,x∈integers}
B={x∣x≤7,x∈integers}
The intersection of these two sets is...
Explanation
First, let's list the members of set A. Set A contains integers between −3 and 8 (exclusive):
A={−2,−1,0,1,2,3,4,5,6,7}
Next, set B contains all integers less than or equal to 7:
B={...,−3,−2,−1,0,1,2,3,4,5,6,7}
The intersection of two sets (A∩B) is the set containing elements that are present in both sets.
Since all members of set A (from −2 to 7) are also contained in set B, the intersection is set A itself:
A∩B={−2,−1,0,1,2,3,4,5,6,7}
Converting this back to set-builder notation, the elements are integers greater than −3 and less than or equal to 7:
A∩B={x∣−3<x≤7,x∈integers}