437 views
0 votes
0 votes
Prove or disprove the following: for finite sets A and B, $\overline{(A - B) \cup (B - A)} = A \cap B$ . If the proposition is incorrect, do minimal modifications to the same and prove.

2 Answers

0 votes
0 votes
LHS = (A∩B) U (Universe - AUB)

RHS = A∩B

so ...statement is incorrect ..

For statement to be correct, a small modification which can be done is AUB = Universe, that is, A and B are exhaustive ..

Related questions

0 votes
0 votes
1 answer
1
dd asked Feb 22, 2017
437 views
Prove the following: $3 \; | \;\left ( a^2+b^2 \right )$ if and only if $3 \; | \;a$ and $3 \; | \;b$.
0 votes
0 votes
0 answers
2
dd asked Feb 22, 2017
317 views
Let $w \in \sum$$*$ be a string, with $\sum$ being the alphabet. Let $w^R$ be the reversal of string $w$, using induction prove that $(w^R)(w^R). . .(\text{for k times}) ...
0 votes
0 votes
2 answers
3
dd asked Feb 26, 2017
540 views
The following is a sequence of formula,$$\begin{align*} \begin{matrix} & 9*1+2 &= &11 \\ & 9*12+3 &= &111 \\ & 9*123+4 &= &1111 \\ & 9*1234+5 &= &11111 \\ \end{matrix} \\...
0 votes
0 votes
2 answers
4
dd asked Feb 25, 2017
494 views
Prove or disprove: $\begin{align*} \log_8x = \frac{1}{2}.\log_{2}x \end{align*}$.