Question: For each argument, please type the statement in symbolic form using: ~ for negation, & for conjunction, v for disjunction, an arrow -> for conditional,
For each argument, please type the statement in symbolic form using:
~ for negation, & for conjunction, v for disjunction, an arrow -> for conditional, and a double arrow for biconditional, and then evaluate the relevant truth/falsity of the overall statement. Feel free to modify the dimensions of the yellow tables if necessary for your answers.
You can use the following table as a guide for evaluating the truth value of each operator.
| p | q | p & q | p v q | p -> q | p q |
| T | T | T | T | T | T |
| T | F | F | T | F | F |
| F | T | F | T | T | F |
| F | F | F | F | T | T |
Example problem:
TRUE STATEMENT: M: Millie washes the car.
FALSE STATEMENT: B: Bill washes the car.
Statement to evaluate: "It is not the case that if Bill washes the car, then Millie washes the car."
This statement can be expressed logically as ~(B -> M). Place this statement in the cells in the first row of the table below and then evaluate the truth value of the overall statement similar to how it was done in the Class 4b video.
| ~ | (B | -> | M) |
| F | T | ||
| F | T | T | |
| F | F | T | T |
| Overall statement: | FALSE |
So, the overall truth value of this statement is FALSE, because the negation outside of the parentheses is false.
TRUE STATEMENTS: M: Mary sings, B: Bob sings, C: Carlita dances
FALSE STATEMENTS: D: Don dances
- Statement to evaluate: "Mary sings and Bob sings."
| Overall statement: |
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