Mathematics - Algebra

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31. The universal relation A x A on A is

A
an equivalence relation
B
anti-symmetric
C
a partial ordering relation
D
not symmetric and not anti-symmetric

Answer
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Option : A
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32. Total number of different partitions of a set having four elements is

A
16
B
8
C
15
D
4

Answer
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Option : C
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33. A partition of {1, 2, 3, 4, 5} is the family

A
((1, 2),(3, 4),(3, 5))
B
(φ(1, 2),(3, 4),(5))
C
{(1, 2, 3),(5)}
D
{(1, 2,), (3, 4, 5)}

Answer
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Option : D
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34. The matrices commute under the multiplication and

commute under the multiplication

A
if a = b (or) θ = nπ, n is an integer
B
always
C
never
D
if a cos θ ≠ b sin θ

Answer
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Option : A
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