Question

Let p, q, and r represent the following simple statements.

p: I study.
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q: I pass the class.
r: I graduate.
Write the following compound statement in its symbolic form.
I graduate if and only if I pass the class, and I study.
The symbolic form is

Answer 1

The compound statement 'I graduate if and only if I pass the class, and I study' can be represented symbolically as p ∧ q → r. This means that studying and passing the class are necessary conditions for graduating.

Step-by-step explanation:

The compound statement 'I graduate if and only if I pass the class, and I study' can be represented symbolically as p ∧ q → r, where ∧ represents 'and', → represents 'implies', and p, q, and r are simple statements representing 'I study', 'I pass the class', and 'I graduate' respectively.

This can be further explained using truth tables. If p, q, and r are true, then the compound statement is true. However, if either p or q is false, the statement is false. For example, if a student does not study (p is false) or does not pass the class (q is false), they will not graduate (r is false).

Learn more about Symbolic representation of compound statements