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21. Which of the following statements is false ?
If R is reflexive, then R ∩ R-1 ≠ φ
R ∩ R-1 ≠ φ =>R is anti-symmetric.
If R, R' are equivalence relations in a set A, then R ∩ R' is also an equivalence relation in A.
If R, R' are reflexive relations in A, then R - R' is reflexive
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22. If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R (= R2) is
R itself
{(1, 2),(1, 3),(3, 3)}
{(1, 3),(2, 3),(3, 3)}
{(2, 1),(1, 3),(2, 3)}
23. If * is defined on R* as a * b = '
1
2
1/2
1/3
24. The identity element in the group with respect to matrix multiplication is
with respect to matrix multiplication is
25. A subset H of a group (G,*) is a group if
a,b ∈ H=> a * b ∈ H
a ∈ H => a-1 ∈ H
a,b ∈ H=> a * b-1 ∈ H
H contains the identity element
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'
