(a) {¬Av ¬B, ¬A-→B, ¬А лB} (b) {¬Av¬B,¬AB, A→B}
explain the answer too
Solution-
Truth table: For the above solution an truth table with its properties is created with proper solution and given as-
1. logical identity
An operation on a single logical value, usually the value of a proposition that, according to logic,
if its operand is true, it returns a value of true; if it is false, it returns a value of false.
The truth table for the logical identity operator is given as: ( number of alphabhet = 2 i.e A,B so n =2 hence2^n= 2^2 = 4, number of true false is 4 )
2.logical negation ( denoted as ¬ A )
An action on a single logical value, usually the value of a proposition, known as a logical negation yields a true value if its operand is false and a false value if its operand is true.
The following is the truth table for NOT A, which is also denoted as ¬ A or ~A :
3. logical conjunction ( denoted as A ∧ B)
The operation of a logical conjunction yields the value true if both of its operands are true.It is applied to two values of the logical system, frequently the values of two propositions.
The following is the truth table for the expression A AND B (also written as A ∧ B, A & B, or A B):
4.Logical disjunction (denoted as A ∨ B )
The operation of logical disjunction, which yields the value true if at least one of its operands is true, operates on two logical values, often the values of two propositions.
The following is the truth table for the expressions A OR B, also denoted as A ∨ B, A || B, or A + B:
5. logical implication(denoted as A implies B or A-> B )
A logical action on two logical values, often the values of two propositions, that results in a value of false merely in the solitary instance where the first operand is true and the second operand is false, is associated with both logical implication and the material conditional.
The truth table for the logical implication A implies B (symbolised as A implies B) and the material conditional if A then B is as follows:
Step by step
Solved in 2 steps with 6 images
