Q1
Let M_2 be the set of square matrices of order 2 over
the real number system and
R={(A,B)∈M_2 ×M_2 ∣A=P^( T) BP for some
non-singular P ∈M}
Then R is
(A) symmetric
(B) transitive
(C) reflexive on M_2
(D) not an equivalence relation on M_2
Q2
For any integer n, let I_n be the interval (n, n+1).
Define
R={(x, y)∈R∣both x, y ∈ I_n for some n∈Z}
Then R is
(A) reflexive on R
(B) symmetric
(C) transitive
(D) an equivalence relation
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