NIMCET 2015 — Mathematics PYQ

• $(P-Q)$: This represents the elements that are in $P$ but not in $Q$. In a Venn diagram, this is the "left crescent" of circle $P$.

• $(Q-P)$: This represents the elements that are in $Q$ but not in $P$. This is the "right crescent" of circle $Q$.

• $(P\cap Q)$: This represents the elements common to both $P$ and $Q$. This is the "middle overlapping region."

2. Combine the sets using Union ($\cup$):

The union operation combines all the elements from the specified regions.

• When you take the elements only in $P$, the elements only in $Q$, and the elements in both, you are essentially covering every part of both circles.

• The combination of "Only $P$", "Only $Q$", and "Both $P$ and $Q$" is the definition of the Union of $P$ and $Q$.

3. Mathematical Identity:

We know that:

And:

Conclusion:

The expression simplifies to $P\cup Q$.