Identify the quantifier in the statement " There exists a capital city for every state of India"
There exists
For every
Both a and b
None of these
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
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 ' Accountancy is a required subject for chartered 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
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 wil not become wealthy.
If you will not become wealthy, then you will not work hard
Write the converse of the statement " If you drink milk, you will be strong".
If you are strong, then you should drink milk
If you do not drink your milk, then you are not strong
If you are not strong, then you do not drink your milk.
If you are strong, then You do not drink your milk
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 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 beautiful nor 165 cm tall
Only if Ananya is both beutiful and 165 cm tall
If Ananya is beutiful and /or not 165 cm tall.
For any statements, P and q,
P q =
- p V - q
- p V q
p V - q
A ______ is a sentence which is either true or false, but not both.
Statement
Converse statement
inverse statement
contrapositive
