Question

Let p and q represent the following simple statements: p: This is an octopus. q: I work hard. r: The stove is hot. Write the following compound statement in its symbolic form. The stove is hot, if and only if this is an octopus and I do not work hard.

Answer 1

The compound statement 'The stove is hot, if and only if this is an octopus and I do not work hard' is symbolically represented as 'r ⇔ (p ∧ ¬q)' in logical notation.

Step-by-step explanation:

The student is asked to write the following compound statement in symbolic form: The stove is hot, if and only if this is an octopus and I do not work hard. In logical notation, this is represented as an equivalence statement, which is true if both sides are either true or false. The symbols for the given simple statements are:

• p: This is an octopus.
• q: I work hard.
• r: The stove is hot.

The symbol for negation (not) is '¬', and for an 'and' operation is '∧'. The 'if and only if' is symbolized as '⇔'. Therefore, the symbolic form of the compound statement is r ⇔ (p ∧ ¬q). This reads as 'r if and only if p and not q' which translates to 'The stove is hot if and only if this is an octopus and I do not work hard'.