1
WB JEE 2021
+1
-0.25
Let A, B, C be three non-void subsets of set S. Let (A $$\cap$$ C) $$\cup$$ (B $$\cap$$ C') = $$\phi$$ where C' denote the complement of set C in S. Then
A
A $$\cap$$ B = $$\phi$$
B
A $$\cap$$ B $$\ne$$ $$\phi$$
C
A $$\cap$$ C = A
D
A $$\cup$$ C = A
2
WB JEE 2021
+2
-0.5
Let R be the real line. Let the relations S and T or R be defined by

$$S = \{ (x,y):y = x + 1,0 < x < 2\} ,T = \{ (x,y):x - y$$ is an integer}. Then
A
both S and T are equivalence relations on R
B
T is an equivalence on R but S is not
C
neither S nor T is an equivalence relation on R
D
S is an equivalence relation on R but T is not
3
WB JEE 2020
+1
-0.25
Let the relation p be defined on R by a p b holds if and only if a $$-$$ b is zero or irrational, then
A
p is equivalence relation
B
p is reflexive and symmetric but is not transitive
C
p is reflexive and transitive but is not symmetric
D
p is reflexive only
4
WB JEE 2020
+2
-0.5
Let p1 and p2 be two equivalence relations defined on a non-void set S. Then
A
both p1 $$\cap$$ p2 and p1 $$\cup$$ p2 are equivalence relations
B
$${p_1} \cap {p_2}$$ is equivalence relation but $${p_1} \cup {p_2}$$ is not so
C
$${p_1} \cup {p_2}$$ is equivalence relation but $${p_1} \cap {p_2}$$ is not so
D
neither $${p_1} \cap {p_2}$$ nor $${p_1} \cup {p_2}$$ is equivalence relation.
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