Answer to Question #123540 in Discrete Mathematics for Muhammad Hasnain

Question

Part (a): Let Aand B are any sets then show that A-(A∩B)=(A∩A^c)∪(A∩B^c) by using membership table.
Part (b): Draw Venn diagram to describe sets A, B, and C that satisfy the given conditions.

A∩B≠ϕ,B∩C≠ϕ,A∩C=ϕ,A⊈B,C⊈B.
Part (c): Find negation of the following statement: If cows are crows then crows are four legged.

Answer 1

$\begin{matrix} A&B&C&A^c&(A \land B^c) (A \land A^c) \end{matrix}$

$\begin{matrix} 0 & 0 & 0 & &1 &&0 &&&0\\ 0 &0 &1 & &1 &&0 &&&0\\ 0& 1&0 && 1&&0 &&&0\\ 0&1&1&&1&&0&&&0\\ 1&0&0&&0&&1&&&0\\ 1&0&1&&0&&1&&&0\\ 1&1&0&&0&&0&&&0\\ 1&1&1&&0&&0&&&0 \end{matrix}$

$\begin{matrix} (A\bigwedge B^c)\lor(A\lor A^c) &&A-(A\land B)\\ 0 &&0\\ 0&&0\\ 0&&0\\ 0&&0\\ 1&&1\\ 1&&1\\ 0&&0\\ 0&&0 \end{matrix}$

P:if cows are crows

Q:crows are four legged

$\begin{matrix} P & Q&&(P\implies Q) && \neg(P\implies Q)\\ T&T&T&&&F\\ T&F&T&&&F\\ F&T&T&&&F\\ F&F&F&&&T \end{matrix}$