Relations And Functions
If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P.
Are these two products equal?
Relations And Functions
If (x + 1, y – 2) = (3,1), find the values of x and y
Sets
Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty
sets and A ∩ B ∩ C = φ.
Sets
Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set
X, show that A = B
Sets
Show that A ∩ B = A ∩ C need not imply B = C.
Sets
Using properties of sets, show that
(i) A ∪ ( A ∩ B ) = A (ii) A ∩ ( A ∪ B ) = A.
Sets
Show that for any sets A and B,
A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )
Sets
Show that if A ⊂ B, then C – B ⊂ C – A.
Sets
Show that the following four conditions are equivalent :
(i) A ⊂ B(ii) A – B = φ (iii) A ∪ B = B (iv) A ∩ B = A
Sets
Let A, B, and C be the sets such that A ∪ B = A∪ C and A ∩ B = A ∩ C. Show
that B = C.
