Question

4. State precisely (but concisely) what it means for two statement forms to be logically equivalent.

Explain proposition, compound statements and basic logical operations with examples. (9)

Answer 1

Answer 4:

What it means for two statement forms to be logically equivalent?

Two statements forms to be logically equivalent if they have the same truth value for all possible combinations of truth values for all variables appearing in the two statements. In this case, we write X≡Y and say that X and Y are logically equivalent.

Proposition statements:

Proposition has a truth value — it makes an assertion that could be true or false. or in simple words, A proposition or statement is a sentence which is either true or false.

Example:

• "Man is Mortal", it returns truth value “TRUE”
• "12 + 9 = 3 – 2", it returns truth value “FALSE”

Compound statements:

A compound statement consists of simpler statements, which are linked together by the use of the linking words - and, or, not, and if-else.

Example:

• 15 is a multiple of 3 or 6.
• A square has four sides and all it’ s sides are equal.

Basic logic operations:

The basic logic operations are as follows:

• Conjunction or AND operation
• Disjunction or OR operation
• Negation or Not operation

Suppose A and B are two boolean variables, then we can define the three operations as;

• A conjunction B or A AND B, satisfies A ∧ B = True, if A = B = True or else A ∧ B = False.
• A disjunction B or A OR B, satisfies A ∨ B = False, if A = B = False, else A ∨ B = True.
• Negation A or ¬A satisfies ¬A = False, if A = True and ¬A = True if A = False

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