State whether the sets $P = \{1, 2, 3, 4\}$ and $Q = \{a, b, c, d\}$ are equivalent sets or not.

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Solution

Two sets are said to be equivalent if they have same cardinal number, i.e., same number of elements in it.
Cardinal number for set $P$ (number of elements in set) will be $n (P) = 4$ .
Cardinal number for set $Q$ (number of elements in set) will be $n (Q) = 4$ .
Since, $n (P) = n (Q)$ .
Hence the sets will be equivalent, $P \leftrightarrow Q$ .

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