Can somebody please explain how to fill out a truth table?
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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.

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.

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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