Question

If the truth value of A v B is true, then truth value of ~A ∧ B can be ___________

1 point

a) True if A is false

b) False if A is false

c) False if B is true and A is false

d) False if A is true and B is false​

Answer 1

Answer:

option c is correct..........

Answer 2

If A v B is true then, ~A^B  is (d)False if A is true and B is false.

Explanation:

• Here the 'v' operator represents boolean OR, '^' represents boolean AND, and '~' represents compliment that is boolean NOT.
• Now we know that boolean OR is true only if at least one of the operands is true.
• Hence, if A v B is true either A is true or B is true or both are true.  
• If A is true B is false then, ~A will be false. Therefore, ~A ^ B will also be false.
• If A is false, B is true then, ~A will be true. Therefore, ~A ^ B will also be true.
• If both are true then, ~A will be false. Therefore, ~A ^ B will also be false.