Conjunction : The Truth Value of a Compound Statement with Conjunction

A joint statement to the effect that each constituent of the statement is true, is compounded by the use of the connective AND. For example, if p stands for the statement “price is rising” and q for “the quantity of money is increasing”. Then the compound statement pq indicates that “the prices are rising and the quantity of money is increasing”. A compound statement of two statements will be true only when both the constituent are true and not when either of them is true or when both are not true. The truth value of a compound statement with conjunction will be as follows:

The first thing to note in the above is that with 2 statements there are 4 combination. In case there are three statements, the possible combination will be 8.

The second is that the basic truth values in the first two columns are 4, 3, 2, 1 in binary digits if the place 1 for T and F. In case there are three statements then the order will be 7, 6, 5, 4, 3, 2, 1, and 0. However, the order can be reversed there is no special sanctity attached to it.

The third is that in the output column, which is the third column in the above table the truth of the compound statement is indicate by T. wherever the alternative combinations are not in keeping with the relationship, F is written.

An electronic circuit in case of this operation will be in the same series so that the impulse from the initial point S1 will not pass to the terminal point S2 if either of the switches is open. See the circuit below….

I think you understand this topics about conjunction. Best of luck.

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Truth table : Truth value of a compound statement constituting several statements

Definition Of Truth Table

Truth table is a table indicating the truth value of a compound statement constituting several statements. The statements are compounded by various connectives e.g. …… AND, OR & NEGATION etc. each one has a significance and therefore the truth of compound statement has to be considered taking these into considerations.

• A truth table has a number of columns and rows. The number of columns depends upon the number of constituent elements and how involved over their relationships. 

• The initial columns, two or three depending on the constituent statements. These give all possible combinations of the constituent statements.

• The remaining columns are the output columns giving the truth values of the compound statement as a function of certain relationship between constituent statements.

• The number of rows in a truth table is determined on the basis of the constituent statements. In case of 2 constituent statements, there are 4 rows and for 3 constituent statements, there are 8 rows.

The truth table is very useful in finding out the validity of an equivalence relation between function. For practical purpose, they help in designing and testing the electronic circuits to perform a given operation based on a certain relationship.

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