solve a, b, and c 2. We want to find S so ((A = B)A A) = S is a tautology.AB(A= B) ^ ATTTFFTFFS((A= B) A A) =→ S(a) In order for ((A= B) ^ A) = S to be a tautology, what must thetruth values of S be? Include all possibilities.(b) Write down two simple statements A and B. (They should bestatements whose truth value can be easily determined)(c) Use your simple statements give an example, in ordinary language,of (A = B) A A.(d) Using your ordinary language statement of (A = B) A A, whatmight you conclude?(e) What does this suggest S should be?(f) Verify that your choice of S makes ((A = B)AA) → Sa tautology.

Answered: 2. We want to find S so ((A → B) ^ 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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Related questions

Question

solve a, b, and c

2. We want to find S so ((A = B)A A) = S is a tautology.
AB(A= B) ^ A
TT
TF
FT
FF
S
((A= B) A A) =→ S
(a) In order for ((A= B) ^ A) = S to be a tautology, what must the
truth values of S be? Include all possibilities.
(b) Write down two simple statements A and B. (They should be
statements whose truth value can be easily determined)
(c) Use your simple statements give an example, in ordinary language,
of (A = B) A A.
(d) Using your ordinary language statement of (A = B) A A, what
might you conclude?
(e) What does this suggest S should be?
(f) Verify that your choice of S makes ((A = B)AA) → Sa tautology.

Expert Solution

Step 1

A proposition of the form “if p then q” or “p implies q”, represented “p => q” is called a conditional proposition. The proposition p is called hypothesis or antecedent, and the proposition q is the conclusion or consequent. Note that p → q is true always except when p is true and q is false.

in other word , "p=>q" means that p is at least as true as q