JEE 2023 Mathematics PYQ — If and be three propositions, then which of the following combina… | Mathem Solvex | Mathem Solvex
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JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023
If p,q and r be three propositions, then which of the following combination of truth values of p,q and r makes the logical expression {(p∨q)∧((∼p)∨r)}→((∼q)∨r)false?
Choose the correct answer:
A.
p=T,q=T,r=F
B.
p=T,q=F,r=T
Correct Answer:
p=F,q=T,r=F
Explanation
Solving:
Ek implication A→B=F tabhi hota hai jab A=T aur B=F ho.
Step 1: Right side (B) ko False set karein
(∼q∨r)=F
⟹∼q=Fandr=F
⟹q=T,r=F
Step 2: In values ko Left side (A) mein rakh kar True set karein
{(p∨q)∧((∼p)∨r)}=T
{(p∨T)∧((∼p)∨F)}=T
{T∧(∼p)}=T
⟹∼p=T
⟹p=F
Conclusion:
Values: p=F,q=T,r=F
Correct Option: (3)
Explanation
Solving:
Ek implication A→B=F tabhi hota hai jab A=T aur B=F ho.
Step 1: Right side (B) ko False set karein
(∼q∨r)=F
⟹∼q=Fandr=F
⟹q=T,r=F
Step 2: In values ko Left side (A) mein rakh kar True set karein
