If the values of p. q, rame (T. F. T), (F. T. T), then what will be the truth value of the expression p V (- q - > p ^ r)in each case?

The correct answer is Option 4) [T, T].

Key Points

• We are given two sets of values for (p, q, r):
  • Case 1: (T, F, T)
  • Case 2: (F, T, T)
• The expression is: p ∨ (¬q → (p ∧ r))
• We'll evaluate it step-by-step for both cases.

Case 1: p = T, q = F, r = T

• ¬q = T (since q is F)
• p ∧ r = T ∧ T = T
• ¬q → (p ∧ r) = T → T = T
• p ∨ T = T ∨ T = T

Case 2: p = F, q = T, r = T

• ¬q = F
• p ∧ r = F ∧ T = F
• ¬q → (p ∧ r) = F → F = T (implication is true when antecedent is false)
• p ∨ T = F ∨ T = T

Final result: [T, T]

Additional Information

• ¬q means logical NOT of q.
• → (implication) is only false when LHS is true and RHS is false.
• ∨ (OR) is true if at least one operand is true.
• ∧ (AND) is true only if both operands are true.