Write the converse of the contrapositive of P q.
P q
q p
~p ~q
~q ~p
If two statements are combined by the word " and". the resulting statement is called
Conjunction
Disjunction
Negation
None of these
Identify the quantifier in the statement " There exists a capital city for every state of India"
There exists
For every
Both a and b
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.
Let P be " Ananya is beautiful", and q be " Ananya is 165 cm tall" under what conditions is the statement, " Ananya is beautiful and 165 cms tall". true?
If Ananya is not beautiful and/or not 165 cm tall.
Only if Ananya is neither beautiful nor 165 cm tall.
Only if Ananya is both beautiful and 165 cm tall
If Ananya is beautiful and/or not 165 cm tall.
Write the contrapositive of the inverse of P q
pq
qp
~p~q
~q~p
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
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
You will become wealthy only if you work hard.
If you will not work hard, then you will not become wealthy.
If you will not become wealthy, then you will not work hard
p: you will work hard, q : you will become wealthy. Translate ( ~p) ( ~q) into an English sentence.
If you will become wealthy, then you will work hard
If you will not become wealthy, then you will not work hard.
Let P be " Shruti can type", and let q be " Shruti takes short hand". Write the statement Shruti can type and take shorthand in symbolic form.
PΛ q
p V q
~ (p V q)
- P Λ - q
