In this activity, you want to find a statement S so that ((Av B)^¬A) → S is a tautology. (a) Complete the column (A V B) ^ ¬A in the table. ((A V B) ^ ¬A) = S AB(AV B) ^¬A TT TF FT F F S (b) In order for (A v B) ^ ¬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 (A V B) ^ ¬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) → Sa tautology.
In this activity, you want to find a statement S so that ((Av B)^¬A) → S is a tautology. (a) Complete the column (A V B) ^ ¬A in the table. ((A V B) ^ ¬A) = S AB(AV B) ^¬A TT TF FT F F S (b) In order for (A v B) ^ ¬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 (A V B) ^ ¬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) → Sa tautology.
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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Question
I need you to only sold the sub parts e, f, and g.
Transcribed Image Text: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
Step 1
The following laws are used to simplify the given logical expression.
- Commutative law: .
- Distribution law: .
- Double negation law: .
- Redundancy law: .
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