Question

If A={a,b,c,d,e}, B={a,c,e,g} and C={b,d,e,g} then which of the following is true?

• A. $C\subset (A\cup B)$
• B. $C\subset (A\cap B)$
• C. $A\cup B=A\cup C$
• D. Both(1) and (3)

Answer 1

The correct option is D Both(1) and (3)

For the given sets,
$(A\cup B)=$ { $a,b,c,d,e,g$} (Combination of all elements of both sets)
Clearly, elements of C are a part of $A\cup B$ as well,
So, $C\subset (A\cup B)$
And, $(A\cap B)=$ { $a,c,e$} (Common elements of both sets )
As the elements of C are not completely a part of $A\cap B$ , Option B is not True.
Also,
$(A\cup C)=$ { $a,b,c,d,e,g$}
Clearly, $(A\cup B)=(A\cup C)$
Hence, both first option and third options are True.