Question

construct a truth table for the following statement form(p → (q →r) ↔( (p n q) →r

Answer 1

Answer:

Another way to write this problem step by step would look like this:

(~p∧q)∨p

=(~T∧F)∨T

=(F∧F)∨T

=F∨T

=T

Step-by-step explanation:

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Answer 2

The figure shows the truth table for the statement,

$\displaystyle\sf{[p\implies (q\implies r)]\iff[(p\land q)\implies r]}$

which seems true in all cases.

Make 8 cases with the statements $\displaystyle\sf {p,\ q}$ and $\displaystyle\sf {r}$ and make decisions for $\displaystyle\sf {q\implies r}$ and then $\displaystyle\sf {p\implies (q\implies r)}$ by using the formula,

$\displaystyle\longrightarrow\sf{p\implies q\equiv\lnot p\lor q}$

Also make decisions for $\displaystyle\sf {p\land q}$ and then for $\displaystyle\sf {(p\land q)\implies r,}$ and finally for $\displaystyle\sf {[p\implies (q\implies r)]\iff[(p\land q)\implies r].}$