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Mathematics
Problem
For a set with
n
n
n
(
n
≥
2
)
(n\ge 2)
(
n
≥
2
)
elements, which of the following expressions equals the number of symmetric but not reflexive relations on the set? a)
2
n
(
n
−
1
)
2
+
n
−
1
2^{\frac{n(n-1)}{2}+n}\; -\; 1
2
2
n
(
n
−
1
)
+
n
−
1
b)
2
n
(
n
−
1
)
2
+
n
2^{\frac{n(n-1)}{2}+n}
2
2
n
(
n
−
1
)
+
n
c)
2
n
(
n
−
1
)
2
+
n
−
2
n
(
n
−
1
)
2
2^{\frac{n(n-1)}{2}+n}\; -\; 2^{\frac{n(n-1)}{2}}
2
2
n
(
n
−
1
)
+
n
−
2
2
n
(
n
−
1
)
d)
2
n
(
n
−
1
)
2
+
n
−
2
n
2^{\frac{n(n-1)}{2}+n}\; -\; 2^{n}
2
2
n
(
n
−
1
)
+
n
−
2
n
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