Definition Of Disjunction And its Uses

A joint statement asserting that at least one of the constituent statements is true, so that more then one constituent statements can also be true, certainly all are not false is compounded by the use of ‘either…… or’ or simply OR. A compound statement of two statements will be true if either of them is true or both are true. It p stands for the optional Maths, and q for the optional Statistics, p OR q will signify;

P and q   Maths and Statistics
P and ~q Maths and not Statistics
Q and ~p Statistics and not Maths

This relationship will be brought out more clearly by the following truth table which may be compared with the previous one to grasp the difference.

As shown above p or q is false only when both p and q are false. This obviously is an inclusive type of disjunction which covers also the situation when both are true.
The plain circuit depicting the relationship is given here under:

The electrical impulse from initial point S_1 will not pass to the terminal point S_2 only when both the switches p and q are open (i.e. off)

The exclusive type of disjunction, which keeps out the situation when all the constituent statement are true, is indicated by p OR q or p+q. In this case the first row of the truth table 4 will have F in the output column. Its circuit will be of the following type :

The exclusive type of disjunction which conveys the sense of “p or q but not both“ is a special case of OR connective. Therefore, unless otherwise stated, p OR q will be taken in the inclusive sense which will always mean “p OR q or both” or “p and/or q”

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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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