Consider the statements:
P : you will work hard, q : you will become wealthy. Translate q P into an English sentence.
If you work hard, then you will become wealthy
If you will become wealthy, then you will work hard.
If you will not work hard, then you wil not become wealthy.
If you will not become wealthy, then you will not work hard
Let P be " Ananya is neutiful", and q be " Ananya is 165 cms tall" under what conditions is the statement, " Ananya is beautiful or 165 cms tall". false?
If Ananya is not beautiful and / or not 165 tall
Only if Ananya is neither beutigul not 165 cm tall
Only if Ananya is both beutiful and 165 cm tall
If Ananya is beutiful and /or not 165 cm tall.
Let P be " shruti can type", and let q be " Shruti takes short hand". Write the statement Shruti can type and take shorthand in sybolic form.
PΛ q
p V q
~ (p V q)
- P Λ - q
Let P be " Shruti can type", and let q be " Shruti takes short hand". Write the statement ' Shruti can never type nor take short hand' in symbolic form.
pV q
PΛ~q
~PΛq
~ P Λ ~q
Symbolise the statement " The square root of all prime numbers are irrational numbers" ( P → set of prime numbers, Q that of irrational numbers).
x Q : x = √x
x Q, x = √x
x P, √x Q
x P, √x Q.
Write the contrapositive of the inverse of P q
pq
qp
~p~q
~q~p
Symbolise the statement ' There exist atleast one number in the set of natural number which is equation to its cube'.
x N, x = x3
x W, x = x3
Write the statement ' According is a required subject for characred Accountants (m) but not for engineers (n). in symbolic form using the leter in parentheses to represent the corresponding component.
mΛ N
m V n
m ~ n
m Λ ~n
For any statements, P and q,
P q =
- p V - q
- p V q
p V - q
Write the converse of the contrapositive of P q.
P q
q p
~p ~q
~q ~p
