Which of the following statement is false :
(a) \(A-B=A\cap B’\)
(b) \(A-B=A-(A\cap B)\)
(c) \(A-B=A-B’\)
(d) \(A-B=(A\cup B)-B\)
Solution
Using set identities,
\[ A-B=A\cap B’ \]
So, option (a) is true.
Also,
\[ A-(A\cap B)=A\cap(A\cap B)’ \]
\[ = A\cap(A’\cup B’) \]
\[ = A\cap B’ \]
\[ = A-B \]
Hence, option (b) is true.
Now,
\[ (A\cup B)-B \]
\[ =(A\cup B)\cap B’ \]
\[ =A\cap B’ \]
\[ =A-B \]
So, option (d) is true.
But,
\[ A-B’ = A\cap(B’)’ \]
\[ =A\cap B \]
which is not equal to \(A-B\).
Answer
\[ \boxed{A-B=A-B’} \]
Correct option: (c)