Convert each statement below into symbolic form and generate its truth table:
If the New York Yankees win the world series or the New York Jets win the super bowl then New York fans will be overjoyed and dance in the streets.
Y: The New York Yankees win the world series.
J: The New York Jets win the super bowl.
O: New York fans will be overjoyed.
D: New York fans will dance in the streets.
(Y ν J) -> (O Λ D)
I agree.
Could it also be (Y Λ J) -> (O Λ D)?
To convert the statement into symbolic form, we can assign the following symbols:
Y: The New York Yankees win the world series.
J: The New York Jets win the super bowl.
O: New York fans will be overjoyed.
D: New York fans will dance in the streets.
The given statement "If the New York Yankees win the world series or the New York Jets win the super bowl then New York fans will be overjoyed and dance in the streets" can be represented symbolically as:
(Y OR J) -> (O AND D)
To generate the truth table for this statement, we need to consider all possible combinations of truth values for Y, J, O, and D, and evaluate the resulting truth value of the statement for each combination.
Here's the truth table for the given statement:
| Y | J | O | D | (Y OR J) | (O AND D) | (Y OR J) -> (O AND D) |
|---|---|---|---|----------|-----------|----------------------|
| T | T | T | T | T | T | T |
| T | T | T | F | T | F | F |
| T | T | F | T | T | F | F |
| T | T | F | F | T | F | F |
| T | F | T | T | T | T | T |
| T | F | T | F | T | F | F |
| T | F | F | T | T | F | F |
| T | F | F | F | T | F | F |
| F | T | T | T | T | T | T |
| F | T | T | F | T | F | F |
| F | T | F | T | T | F | F |
| F | T | F | F | T | F | F |
| F | F | T | T | F | T | T |
| F | F | T | F | F | F | T |
| F | F | F | T | F | F | T |
| F | F | F | F | F | F | T |
In the truth table, T represents true and F represents false. The expression (Y OR J) -> (O AND D) is true in the first, ninth, tenth, eleventh, twelfth, thirteenth, and fourteenth rows and false in the remaining rows.