Answer to Question #281205 in Discrete Mathematics for Anonymous005

Question

Consider two sets A and B such that A ⊆ B. Find the possible values of x if A = {2, 4, 6, x} and B = {2, 3, 5, 6, x+1}. Ans: x = 3. Please explain.

Answer 1

The set $A$ is a subset of $B,$ and $B$ is a superset of $A,$ if and only if every element of $A$ is also an element of $B.$ We use the notation $A ⊆ B$ to indicate that $A$ is a subset of the set $B.$

Compare the set $A$ and set $B.$

$4$ must be the element of $B,x$ must be the element of $B.$

Then $4=x+1$ and $x=3.$ This system has the only solution $x=3.$