Venn Diagrams are named after English Logician John Venn

The Venn Diagrams are named  after  English  Logician  John  Venn (1834-1923)  to present  pictorial  representation. The Universal Set, say  U or X is denoted by a region enclosed by a ractangle and one or more sets say, A, B, C are shown through circuits or closed curves within these rectangles. These circuits or closed curves intersect each other if there are any common elements amongst them, If there are no common elements then they are shown separately as disjionts.

Several set relations can be easily shown by these diagrams. These are useful to illustrate the set relations, such as the subset, set relations and the set-operations such as intersection, union, complemention, etc. by using regions in aplane to indicate sets. But Venn Diagrams (also known as Venn Euler Diagrams) can not be used to prove any statements regarding sets, just as geometric figures can not be used to prove geometric theorems. They are more aids for searching appropiate proofs.    

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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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