Question 3

The number of relations, defined on the set {a, b, c, d}, which are both reflexive and symmetric, is equal to:

Set has 4 elements: {a, b, c, d}. Relations that are both reflexive and symmetric.

Reflexive: must contain (a,a), (b,b), (c,c), (d,d) — 4 pairs fixed.

Symmetric: for each pair (i,j) where i≠j, either both (i,j) and (j,i) are in R, or neither.

Number of unordered pairs from 4 elements: $$\binom{4}{2} = 6$$.

Each can be included or not: $$2^6 = 64$$.

The answer is Option 1: 64.

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