In order to prove an propositional argument invalid it is only necessary to find a propositional model (i.e, an assignment of truth values to the propositional variables) that shows it is possible for all the premises to be true and the conclusion false. Given premises a and b below, determine whether each conclusion 1 - 5 follows by doing a full truth table OR using the short-cut method. Which conclusions do follow from the two premises and which ones do not? Hint: this problem is a little easier if you first convert all implications to disjunctions, as disjunctions are T if any disjunct is T, and only F if all disjuncts are F. Let d = logic is difficult; l = many students like logic; and, m = math is easy. Premises: Logic is difficult or not many students like logic. If math is easy, then logic is not difficult. Conclusions: Mathematics is not easy, if many students like logic. If mathematics is not easy, then not many students like logic. Mathematics is not easy or logic is difficult. Not many students like logic or mathematics is not easy. If not many students like logic, then either mathematics is not easy or logic is not difficult
In order to prove an propositional argument invalid it is only necessary to find a propositional model (i.e, an assignment of truth values to the propositional variables) that shows it is possible for all the premises to be true and the conclusion false. Given premises a and b below, determine whether each conclusion 1 - 5 follows by doing a full truth table OR using the short-cut method. Which conclusions do follow from the two premises and which ones do not? Hint: this problem is a little easier if you first convert all implications to disjunctions, as disjunctions are T if any disjunct is T, and only F if all disjuncts are F. Let d = logic is difficult; l = many students like logic; and, m = math is easy. Premises: Logic is difficult or not many students like logic. If math is easy, then logic is not difficult. Conclusions: Mathematics is not easy, if many students like logic. If mathematics is not easy, then not many students like logic. Mathematics is not easy or logic is difficult. Not many students like logic or mathematics is not easy. If not many students like logic, then either mathematics is not easy or logic is not difficult
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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In order to prove an propositional argument invalid it is only necessary to find a propositional model (i.e, an assignment of truth values to the propositional variables) that shows it is possible for all the premises to be true and the conclusion false. Given premises a and b below, determine whether each conclusion 1 - 5 follows by doing a full truth table OR using the short-cut method. Which conclusions do follow from the two premises and which ones do not?
Hint: this problem is a little easier if you first convert all implications to disjunctions, as disjunctions are T if any disjunct is T, and only F if all disjuncts are F.
Let d = logic is difficult; l = many students like logic; and, m = math is easy.
Premises:
- Logic is difficult or not many students like logic.
- If math is easy, then logic is not difficult.
Conclusions:
- Mathematics is not easy, if many students like logic.
- If mathematics is not easy, then not many students like logic.
- Mathematics is not easy or logic is difficult.
- Not many students like logic or mathematics is not easy.
- If not many students like logic, then either mathematics is not easy or logic is not difficult.
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