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(i)
The negation of the statement:
For every x ∈ N, x + 3 < 10
is
There exists x ∈ N such that x + 3 ≥ 10.
(ii)
There exists x ∈ N, x + 3 = 10
For every x ∈ N, x + 3 ≠ 10
All the students completed their homework.
some of the students did not complete their home work.
There exists a number which is equal to its square.
For every real number x, x2≠ x.
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Chapter 31: Mathematical Reasoning –...