Logical Reasoning with Propositions

This assignment focuses on propositional logic. It presents a series of propositions and truth values (True/False) for variables like L, P, S, W. The task involves evaluating complex expressions using truth tables and determining the validity of conclusions based on given premises. The assignment also includes a specific formula A = S(W^P), which needs to be analyzed in the context of the provided truth values.

Running head: CRITICAL THINKING
Critical Thinking
Name of the Student:
Name of the University:
Author Note

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CRITICAL THINKING
Answer to question number 1
Hypothesise testing
The hypothesis testing is the process that is used for the determination of the
probability of given hypothesis and determines whether the provided hypothesis is true or
not. This is a part of using the statistics. There are various steps that are present in this
procedure:
1. It involves formulating the null hypothesis and also the alternative hypothesis.
2. Identifying the test statistics that would be used for assessing the null hypothesis.
3. Then the step involves computing the P-value for the test hypothesis that would be
considered taking the null hypothesis to be true
4. Comparing the p-value with the significant null value. If the p-value is greater than
the alpha value or the significant value and decided if the hypothesis is true or not.
The example of test hypothesis is analysis of a collection of data. The hypothesis
testing is generally used for the analysis of different type of results. One such instance is
the Lady testing tea example.
Brainstorming
Brainstorming is the procedure where the people are involved in testing their brain
and thinking capabilities. In this type of procedures the people are generally forming a group
and having a deep thinking sessions. A group of people generally get together and think of
solution of a set of problems that are assigned to them. This involves different people
providing different ideas and final steps involves coming into a conclusion about the solution
for the problems.

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CRITICAL THINKING
An example of this technique is the group discussion technique and the board
meetings that take place in the companies. The round table conferences are also form of
brainstorming sessions.
Answer to question number 2
Type Text
Claim a reliable product is totally free of technical errors
Issue Vendors frequently express a product's reliability quotient as a
percentage
Statement Evolutionary products are usually considered to become
increasingly reliable
Argument
Premise/
Conclusion
IBM’s z/OShas a reputation for reliability because it evolved
from a long line of earlier MVS and OS/390 operating system
versions
Answer to question number 3
R S P ((R ∨ S) → ¬p)
F F F T
F F T T
F T F T

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CRITICAL THINKING
F T T F
T F F T
T F T F
T T F T
T T T F
P R (P ∧ ¬R)
F F F
F T F
T F T
T T F
P S (S ∧ (¬S → P))
F F F
F T T

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CRITICAL THINKING
T F F
T T T
((R ∨ S) → ¬p) (P ∧ ¬R) (S ∧ (¬S → P)) R
F F F T
F F T T
F T F T
F T T T
T F F T
T F T T
T T F T
T T T T
Hence, it can be easily said that the conclusion is a valid one.
Answer to question number 4
L S W ((L → ¬S) ∨ ¬W)
F F F T

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CRITICAL THINKING
F F T T
F T F T
F T T T
T F F T
T F T T
T T F T
T T T F
L P (P ∨ ¬L)
F F T
F T T
T F F
T T T
S ¬S
F T

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CRITICAL THINKING
T F
Let A= S (W^P)
P S W (S → (W ∧ P))
F F F T
F F T T
F T F F
F T T F
T F F T
T F T T
T T F F
T T T T
((L → ¬S) ∨ ¬W) (P ∨ ¬L) ¬S A
F F F F
F F T F
F T F F

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CRITICAL THINKING
F T T F
T F F F
T F T F
T T F F
T T T F
The conclusion S (W^P) is invalid for the premises.