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Safari File Edit View History Bookmarks Window Help 0 ng.cengage.com Cengage MindTap Cengage Learning MINDTAP Nam Nguyen" 6.1 Aplia Assignment Due on Mar 18 at 11.59 PM PDT Use your knowledge of propositional logic symbols and translation methods to determine which of the following statements are true. Check the box next to each true statement The statement A B is equivalent to the statement B A. Statements containing the words "not," "it is false that," or "it is not the case that" are usually best translated as negations with the tilde () operator The antecedent of a conditional represents a necessary condition The antecedent of a conditional represents a sufficient condition The following expression is a well-formed formula (WFF): [(M V N) . (N v U)] v (X Y). You should translate the statement "This year's being 2010 is a sufficient and necessary condition for next year's being 2011" into propositional logic notation as TE N; where T stands for "This year is 2010," and N stands for "Next year is 2011." A tilde (~) is the main operator in this statement: ~[(A+ Z) ~(W . P)] You should translate an ordinary language statement with the form "p ifg" into propositional logic notation as qp You should translate the statement "Today is Wednesday unless tomorrow is Friday" into propositional logic notation as W v F; where W stands for "Today is Wednesday," and F stands for "Tomorrow is Friday." The triple bar (E) operator expresses the logical relation of material implication. In propositional logic, the fundamental elements are terms. You should translate the statement "Not both today is wednesday and tomorrow is Friday" into propositional logic notation as ~ w. ~F; where W stands for "Today is Wednesday," and F stands for "Tomorrow is Friday. The statements "A ifB" and "A only if B. do not have the same meaning A dot (*) is the main operator in this statement: ~[(nQ v ~W)·( ~L)] The horseshoe (3) operator expresses the logical function of material implication. A-Z 182 M

Explanation / Answer

1. Statement is True. The sign is used for negation.

3 and 4 are true with regard to the antecedent of a conditional.

6 is a true translation of the relation between the said propositions

7 is true. Tilde is the main operator in the statement

8 is true about ‘p if q’

9 is true about W and F

13. Is a true statement about ‘A if B’ as different from ‘A only if B’

15. is a true statement about the horseshoe symbol

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