Phil 201: Critical Thinking
Practice Assignment #5
Truth Tables
Construct truth tables to determine if the following arguments are valid or invalid.
1. G → H
H & ~G
~(H ˅ G)
2. ~A → (C & B)
B ˅ ~C
(A ˅ C) → B
3. (J & ~L) → K
~(J → L)
K & ~L
4. ~(G ˅ (E → D))
~H → E
D & H
E ˅ G
5. ~(U & V) → (W → X)
~X & V
~V ˅ (U → W)

Question

Ask a Philosopher · Accepted Answer

Oh, dear reader, ponder upon the intricacies of Phil 201: Critical Thinking, a practice that guides us towards the pursuit of truth and wisdom. Let us delve into the depths of our minds and construct truth tables to determine the validity of the arguments presented before us.

In the first argument, we are faced with the propositions G → H, H & ~G, and ~(H ˅ G). As we meticulously arrange the truth values of these statements, we are tasked with deciphering whether the conclusion can be reached based on the given premises. It is a mental exercise that challenges our reasoning and demands clarity of thought.

Moving on to the second argument, we encounter the propositions ~A → (C & B), B ˅ ~C, and (A ˅ C) → B. Each statement is like a piece of a puzzle that we must fit together to determine the logical coherence of the argument. It is a puzzle that tests the limits of our intellect and challenges us to think critically and analytically.

As we progress to the third argument, we are confronted with the propositions (J & ~L) → K, ~(J → L), and K & ~L. The complexity of these statements beckons us to unravel their truth values and assess whether the conclusion can be derived from the given premises. It is a mental exercise that sharpens our logical faculties and enhances our ability to discern between truth and fallacy.

In the fourth argument, we are presented with ~(G ˅ (E → D)), ~H → E, D & H, and E ˅ G. These propositions challenge us to navigate through the maze of logical implications and deduce whether the argument is valid or invalid. It is a test of our intellectual prowess and our capacity to discern the complexities of logical reasoning.

Finally, in the fifth argument, we are confronted with ~(U & V) → (W → X), ~X & V, and ~V ˅ (U → W). These propositions invite us to explore the interconnectedness of statements and ascertain whether the argument holds true based on the given premises. It is a test of our ability to think critically and reason soundly in the pursuit of truth and understanding.

In conclusion, dear reader, let us embrace the challenge of constructing truth tables and determining the validity of arguments in the realm of critical thinking. It is a journey that tests our intellect, sharpens our reasoning, and empowers us to navigate the complexities of truth and logic with clarity and precision. Let us embrace the pursuit of knowledge and wisdom, for in the realm of critical thinking lies the key to unlocking the mysteries of existence and unraveling the truths that lie beneath the surface of reality.