Question

This argument is:J ⊃ C / R ∨ I / I ⊃ (U • ∼ J) / (R ∨ U) ⊃ (C • J) // C
a.Valid
b.InValid

Answer 1

This logic question is about determining the validity of a symbolic argument in Mathematics. The argument given does not directly follow a disjunctive syllogism, and based on the provided premises, the conclusion C does not necessarily follow, suggesting that the argument is invalid.

Step-by-step explanation:

The subject of this question is logical reasoning within the domain of Mathematics, specifically in the area of deductive reasoning. The question involves determining whether a given argument is valid based on its logical form. The argument presented uses symbolic logic:

• 
  
• J ⊃ C
• 
  
• R ∨ I
• 
  
• I ⊃ (U ⋅ ∼ J)
• 
  
• (R ∨ U) ⊃ (C ⋅ J)
• 
  
• /∕ C

To address the validity of the argument, let's examine it using the formula of valid deductive inferences, such as the disjunctive syllogism:

1. 
   
3. X or Y.
4. 
   
6. Not Y.
7. 
   
9. Therefore X.

In this case, the argument does not appear to directly follow a disjunctive syllogism, as no single premise directly negates I or J to conclude U. However, the arguments' validity depends on the interrelations of the premises and whether the rules of logic allow for the conclusion C to be deduced. Without additional premises that would provide such a link, the conclusion C does not necessarily follow from the premises given, and thus the argument, as stated, appears to be invalid. The conclusion would need a premise that connects C to the previously stated premises.