Question

# Can somebody please explain how to fill out a truth table? I think I figured it out for the short formula but am

confused when approaching formulas with multiple variables.

*For questions 21 - 23, **translate **the ordinary language sentence into **symbolic form,** first by writing the corresponding statement represented by each **variable** (A, S, F), and then by rewriting the sentence as a **formula **using **operators** (~ ^ v *⊃⊃* *≡*) and **variables**.*

21. If both the administration's budget increases and student scholarship funding increases, then it

is not true that the faculty budget will increase.

A: The administration's budget increases.

S: The student's scholarship funding increases.

F: The faculty budget increases. ** **

Formula: A^S ⊃ ~F

22. Either the administration's budget increases or student scholarship funding increases.

A: The administration's budget increases.

S: The student scholarship funding increases. ** **

Formula: A v S

23. It is not true that the faculty budget will increase.

F: The faculty budget will increase.

Formula: ~F

*Rewrite the **formulas **from questions 21 - 23 as an **argument **(**premises **and a **conclusion)**, and construct a **long (indirect) method truth table**. Determine whether or not a **counter-example **exists, and write "Valid" or "Invalid."*

24. Premise 1 Premise 2 Conclusion

*Valid or Invalid*

F: __**______________ **A: __**_____________ **S: ________________

*For question 25, rewrite the **formulas **from questions 21 - 23 as an **argument **(**premises **and a **conclusion)**, and construct a **short (direct) method truth table**. Determine whether or not a **counter-example **exists, and write "Valid" or "Invalid."*

25. Premise 1 Premise 2 Conclusion

*Valid or Invalid*

F: ________________ A: ________________ S: ________________

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