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propositional logic part – 2


Definition : let p and q be propositions. The conjuction of p and q denoted by p ^ q is the proposition ” p and q “. The conjuction of p and q is true when both p and q are true . otherwise false.

p q p^q
T T T
T F F
F T F
F F F

Excercise – 3 :

Find the conjuction of proposition p and q where p is the proposition ” Today is Friday  ” and q is the proposition  ” It is raining today ”

Solve :

The conjuction of these propositions is p ^ q is the proposition ” Today is Friday and It is raining today. ” So the proposition is true rainy fridays and false on any day that is not friday or on friday that is not rainy .

Definitions – 3 :

Let p and q be propositions . The disjunction of p and q denoted by p v q is the propositon ” p or q “. The disjunction p v q is false when both p and q are false and is true otherwise.

p q p v q
T T T
T F T
F T T
F F F

Excercise – 6 :

What is the disjunction of the proposition p and q where p is ” Today is friday ” and q is ” It is raining today. ”

Solve :

The disjunction of p and q p v q is the proposition .

” Today is friday or it is raining today.  ”
The proposition is true on any day that is either a friday or a rainy day (including rainy friday). it is only false on days that are not fridays when it does not rain.

 

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