All MCQs

The valid order preserves W before X before Y and Z before V.
Only W, Z, X, V, Y satisfies both chains.

Let the son's age be x and the father's age 2x.
Then 3x = 54, so x = 18.

Every student must receive exactly one identical pen.
There is only one distinguishable final distribution.

The prizes are distinct, so order matters.
The number of assignments is 5×4×3 = 60.

Order does not matter when selecting a committee.
The number of selections is 5 choose 2 = 10.

Each handshake is a unique pair of people.
The number of pairs is 8×7/2 = 28.

Each match corresponds to a unique pair of teams.
The number of pairs is 6×5/2 = 15.

The path from A to D passes through A-B, B-C, and C-D.
That requires three road segments.

Red objects form a subset of large objects, which form a subset of visible objects.
Therefore, red objects must be visible.

A implies B, and B implies C.
By chaining the two rules, A guarantees C.

The contrapositive of P → Q is not-Q → not-P.
It is logically equivalent to the original conditional.

For 3, 5, and 7, squaring and adding 1 gives 10, 26, and 50.
The same rule matches every example.