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Question

Prepare truth table of the following statement patterns.
(i) $$\sim p \rightarrow (q \leftrightarrow p)$$
(ii) $$(q \leftrightarrow p) \vee (\sim p \leftrightarrow q)$$
(iii) $$p \leftrightarrow [\sim(q \vee r)]$$


Solution

(3) $$p\leftrightarrow [\sim(q\vee r)]$$
 p q r $$q\vee$$ r$$\sim(q\vee r)$$ $$p\leftrightarrow [\sim(q\vee r)]$$ 
 0 0
1
 1 1 0 1
 0 0 0 1 1
 1 0 1 0 0
 1 0 1 0 0
 1 1 1 1 0 0
(2) $$(q\leftrightarrow p)\vee(\sim p\leftrightarrow q)$$
 q $$q\leftrightarrow p$$$$ \sim p$$$$ \sim p\leftrightarrow q$$$$(q\leftrightarrow p)\vee(\sim p \leftrightarrow q)$$
 00
0
(1) $$\sim p\leftrightarrow\,\,\,q\leftrightarrow p$$
 p q $$\sim p$$$$q\leftrightarrow p$$  $$\sim p\rightarrow q\leftrightarrow p$$
00
01 1
0
1

Mathematics

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