Question

If p → q is true, then ~ q → ~ p is __________ false.

always
sometimes
never

Answer 1

always true

Answer 2

thnx

Answer 3

the answer is "never" false

Answer 4

\[\begin{array}{cccc}(p&\Rightarrow&q)&\implies (\neg p&\Rightarrow\neg q)\\\hline\top&&\top\\\top&&\bot\\\bot&&\top\\\bot&&\top\end{array}\]

Answer 5

fill in the rest of the truth table

Answer 6

\[\begin{array}{cccc}(p&\Rightarrow&q)&\implies& (\neg p&\Rightarrow&\neg q)\\\hline\top&\top&\top&&\bot&&\bot\\\top&\bot&\bot&&\bot&&\top\\\bot&\top&\top&&\top&&\bot\\\bot&\top&\bot&&\top&&\top\end{array}\]

Answer 7

\[\begin{array}{cccc}\color{red}(p&\color{blue}\Rightarrow&q\color{red})&\color{red}\implies& \color{red}(\neg p&\color{blue}\Rightarrow&\neg q\color{red})\\\hline\top&\color{blue}\top&\top&\color{red}\top&\bot&\color{blue}\top&\bot\\\top&\color{blue}\bot&\bot&\color{red}\top&\bot&\color{blue}\top&\top\\\bot&\color{blue}\top&\top&\color{red}\bot&\top&\color{blue}\bot&\bot\\\bot&\color{blue}\top&\bot&\color{red}\top&\top&\color{blue}\top&\top\end{array}\]

Answer 8

i think i read the question wrong

Answer 9

@UnkleRhaukus the question is ~q -> ~p. it is you that is wrong

Answer 10

sorry

Answer 11

the contrapositive has the same truth value as the implication

Answer 12

\[\begin{array}{cccc}\color{red}(p&\color{blue}\Rightarrow&q\color{red})&\color{red}\implies&\color{red}(\neg q&\color{blue}\Rightarrow&\neg p\color{red})
\\\hline\top&\color{blue}\top&\top&\color{red}\top&\bot&\color{blue}\top&\bot
\\\top&\color{blue}\bot&\bot&\color{red}\top&\top&\color{blue}\bot&\bot
\\\bot&\color{blue}\top&\top&\color{red}\top&\bot&\color{blue}\top&\top
\\\bot&\color{blue}\top&\bot&\color{red}\top&\top&\color{blue}\top&\top\end{array}\]