do not handwrite this. 1. In this activity, you want to find a statement S so that ((AVB)A¬A) =S is a tautology.(a) Complete the column (A V B) A ¬A in the table.((AV B) A¬A) =→ SА В (AV B) л -АTTTFFTF F(b) In order for (AV B) A¬A= S to be a tautology, it must alwaysbe true. What must the truth values of S be for this to happen?(Include all possibilities)(c) Write down two simple statements A and B. (They should bestatements whose truth value can be easily determined)(d) Use your simple statements give an example, in ordinary language,of (AV B) A¬A.(e) Using your ordinary language statement of (A V B) ^ ¬A, whatmight you conclude?(f) What does this suggest S should be?(g) Verify that your choice of S makes ((AVB)A¬A) = Sa tautology.

Answered: In this activity, you want to find a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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do not handwrite this.

1. In this activity, you want to find a statement S so that ((AVB)A¬A) =
S is a tautology.
(a) Complete the column (A V B) A ¬A in the table.
((AV B) A¬A) =→ S
А В (AV B) л -А
TT
TF
FT
F F
(b) In order for (AV B) A¬A= S to be a tautology, it must always
be true. What must the truth values of S be for this to happen?
(Include all possibilities)
(c) Write down two simple statements A and B. (They should be
statements whose truth value can be easily determined)
(d) Use your simple statements give an example, in ordinary language,
of (AV B) A¬A.
(e) Using your ordinary language statement of (A V B) ^ ¬A, what
might you conclude?
(f) What does this suggest S should be?
(g) Verify that your choice of S makes ((AVB)A¬A) = Sa tautology.

Expert Solution

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Consider the statement $((A \lor B) \land \neg A) \Rightarrow S$ is a tautology , therefore it has true truth value. The statement $p \Rightarrow q$ is a conditional statement, its truth values are true always except when $p$ is true and $q$ is false.