Negating "If no one is absent, then if the weather permits, we will study outside" I am a beginner; please help solve this. > Write the negation of the statement: > > "If no one is absent, then if the weather permits, we will study outside."

First, write the statement as a logical statement (with appropriate notation).

A: "No one is absent."

W: "Weather permits"

S: "We will study outside."

Then we have the proposition, symbolically: $$A\rightarrow(W \rightarrow S)$$

Then, since we want to negate the proposition, we work with:

$$\begin{align} \lnot\Big(A\rightarrow(W \rightarrow S)\Big)& \equiv \lnot\Big(\lnot A \lor (\lnot W \lor S)\Big)\tag{$p\rightarrow q \equiv \lnot p \lor q$}\\\ \\\ & \equiv A \land W \land \lnot S\tag{DeMorgan's}\end{align}$$

So the negation of the statement translated back to English gives us:

> "No one is absent and weather is permitting, but (and) we won't study outside."