I need to use the laws of equivalence and rules of inference to show that the statement: "$s\land(r\to\lnot q)$" using the following premises:
- $(r\lor\lnot t)\to p$
- $t \to s$
- $p \to \lnot q$
So far I've worked out
- From $t$ and $t \to s$, we can infer $s$ from modus ponen.
- From $p \to \lnot q$ and $(r\lor\lnot t)\to p$ we can infer $(r\lor\lnot t)\to \lnot q$
But I'm not sure how to get from $r\lor\lnot t$ to just $r$