Venn Diagrams Involving 3 Sets

Each element can either belong or not belong to each of A, B, and C. That gives $2^3=8$ possible combinations.

Only A, Only B, Only C, A and B only, A and C only, B and C only, A and B and C (centre), and Outside all three.

There are exactly 8 distinct regions in a three-set Venn diagram.

A two-set Venn diagram already has 4 regions. Adding a third set creates more overlaps, so 6 is too small.

7 would be correct only for the regions inside the circles, but the region outside all three circles is also a valid region.

Counting carefully gives exactly 8 combinations of membership — there is no 9th possible combination.

8 is correct: $2^3=8$ combinations of being inside or outside each of three sets.

$A\cap B$ means elements in both A and B. $C^{\prime }$ means elements NOT in C.

$A\cap B\cap C^{\prime }$ means elements that are in A AND in B AND NOT in C.

This is the 'A and B only' sliver — elements in both A and B, but excluded from C.

All three sets would be $A\cap B\cap C$, not $A\cap B\cap C^{\prime }$. The prime (') means NOT in C.

'A or B' uses the union symbol $\cup$, not intersection $\cap$. This option confuses union with intersection.

This would be written $C\cap A^{\prime }\cap B^{\prime }$, which is the opposite of what is given.

$A\cap B\cap C^{\prime }$ = elements in A and B but not in C.