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Negation of the statement “All equivalent triangles are isosceles”
P: All equilateral triangles are isosceles.
Some equilateral triangles are not isosceles.
Negation of the statement “Some real numbers are not complex numbers”
P: Some real numbers are not complex numbers.
All real numbers are complex numbers.
Negation of the statement “\(\forall n \in {\text {N}},n + 1 \ge 2\)” is:
P:
are negation of each other.
Negation of the statement “Some quadratic equations have unequal roots” is
P: Some quadratic equations have unequal roots.
All quadratic equations have unequal roots.
“\(\forall x \in {\text{N, }}{x^2}\) + x is an even number”. Find the negation of above statement.
P: is an even number.
is not an even number.
\(\sim \left[ {p \cap \left( {q \to r} \right)} \right]\) is equal to
\(\sim \left[ {\left( {\sim p \cup q} \right) \cap r} \right]\) is equivalence to
Hence, the given statement is not equvalence to option 1, 2 and 3.
\(p \cap \left( {q \cup \sim p} \right)\) is equivalence to
\(\left( {p \cap q} \right) \cup \left( {\sim p \cap q} \right) \cup \left( {\sim q \cap r} \right)\) is equivalence to
\(\sim \left[ {\left( {p \cap q} \right) \to \left( {\sim p \cup r} \right)} \right]\) is equivalence to
Negation of the statement. ” All students of IIT, Bombay live in the hostal.”
P: All students of IIT, Bombay live in the hostel.
Some students of IIT, Bombay do not live in the hostel.
“\(\exists x \in {\text{R, such that }}{x^2} < x \)". Find the negation of above statement.
P: .
“Some continuous functions are differentiable.” Find the negation of above statement.
P: Some continuous functions are differentiable.
All continuous functions are not differentiable.
Negation of the preposition\(\left( {q \cup \sim r} \right) \cap \left( {p \cup q} \right)\) is
Write the negation of the statement. “\( 5 \times 5 = 25 \)”
P: