If (x + 1, y – 2) = (3,1), find the values of x and y
28/10/2024
Mathematics
11th (Science)
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.
28/10/2024
Mathematics
11th (Science)
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
28/10/2024
Mathematics
11th (Science)
Sets
Show that A ∩ B = A ∩ C need not imply B = C.
28/10/2024
Mathematics
11th (Science)
Sets
Using properties of sets, show that
(i) A ∪ ( A ∩ B ) = A (ii) A ∩ ( A ∪ B ) = A.
28/10/2024
Mathematics
11th (Science)
Sets
Show that for any sets A and B,
A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )
28/10/2024
Mathematics
11th (Science)
Sets
Show that if A ⊂ B, then C – B ⊂ C – A.
28/10/2024
Mathematics
11th (Science)
Sets
Show that the following four conditions are equivalent :
(i) A ⊂ B(ii) A – B = φ (iii) A ∪ B = B (iv) A ∩ B = A
28/10/2024
Mathematics
11th (Science)
Sets
Let A, B, and C be the sets such that A ∪ B = A∪ C and A ∩ B = A ∩ C. Show
that B = C.
28/10/2024
Mathematics
11th (Science)
Sets
In each of the following, determine whether the statement is true or false. If it is
true, prove it. If it is false, give an example.
(i) If x ∈ A and A ∈ B , then x ∈ B
(ii) If A ⊂ B and B ∈ C , then A ∈ C
(iii) If A ⊂ B and B ⊂ C , then A ⊂ C
(iv) If A ⊄ B and B ⊄ C , then A ⊄ C
(v) If x ∈ A and A ⊄ B , then x ∈ B
(vi) If A ⊂ B and x ∉ B , then x ∉ A
