In November 2024
Answer to Question #148675 in Discrete Mathematics for Rohit Jaiswal
a) p V ~q
b) ~p V ~q
c) q -->p
d) ~(p-->q)-->r
"\\begin{matrix}\n P & q&\\tilde q &pv\\tilde q\\\\\n T&T&F&T\\\\\n T&F&T&T\\\\\n F&T&F&F\\\\\n F&F&T&T\\\\\n\\end{matrix}\\\\\n\n\\begin{matrix}\n P & \\tilde p& q&\\tilde q &\\tilde pv\\tilde q\\\\\n T&F&T&F&F\\\\\n T&F&F&T&T\\\\\n F&T&T&F&T\\\\\n F&T&F&T&T\\\\\n\\end{matrix}\\\\\n\n\\begin{matrix}\n P & q&q\\implies p\\\\\n T&T&T\\\\\n T&F&T\\\\\n F&T&F\\\\\n F&F&T\\\\\n\\end{matrix}\\\\\n\n\\begin{matrix}\n P & q&r&p\\implies q&\\tilde( p \\implies q)&\\tilde(p\\implies q)\\implies r\\\\\n T&T&T&T&F&T\\\\\n T&T&F&T&F&T\\\\\n T&F&T&F&T&T\\\\\n T&F&F&F&T&F\\\\\n F&T&T&T&F&T\\\\\n F&T&F&T&F&T\\\\\n F&F&T&T&F&T\\\\\n F&F&F&T&F&T\\\\\n\\end{matrix}\\\\"
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