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Conjunction

If two statements p and q are combined by the connective “AND” (), then the compound statement p  q so formed is called a conjunction. For example, if p: he is tall, q: he is handsome, then their conjunction is p  q: he is tall and he is handsome or p  q: he is tall and handsome.
 
Sometimes p  q is also written as pq or p.qp  q is true only when both p and q are true.
 
The following truth table shows the truth values of p  q and q  p.
 
Truth table (p  qq  p)
p
q
p  q
q  p
T
T
T
T
T
F
F
F
F
T
F
F
F
F
F
F
Rule: p  q is true only when both pand q are true.
 
Remark: The above truth table shows that p  q = q  p.




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