How can $(\lnot q \lor r)$ become $(p \to r)$ in this context?

Question

Question

Show that $(p\lor q)\rightarrow r\equiv(p\rightarrow r)\land(p\rightarrow r)$

Given solution

While I was taught that $(p\rightarrow r)\equiv( \neg p\lor r)$ which can be easily proven by a truth table...

but how is the last 2 statements in the given solution be possible? How is it possible that $(\neg q\lor r)$ transformed into $(p\rightarrow r)$? Is this a typo?

Yes. It's a typo. It should read $q\to r$. – b00n heT Sep 16 '19 at 11:04 — b00n heT, Sep 16 '19 at 11:04

score 1 · Accepted Answer · answered Sep 16 '19 at 11:16

1

It's a typo. See here for the tableau of the intended statement

enter image description here

answered Sep 16 '19 at 11:16

Shaun

44,997

How can $(\lnot q \lor r)$ become $(p \to r)$ in this context?

Question

Given solution

1 Answers1