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TRUE OR FALSE ? Justify your answer. a. There exist real numbers a and b such (a+b)^2 = a^2 + b^2. b. For any real number x, th...Asked by Alfonso
TRUE OR FALSE ? Justify your answer.
a. There exist real numbers a and b such (a+b)^2 = a^2 + b^2.
b. For any real number x, there exists a unique number -x such that x + (-x) = 0.
c. Any integer n is either odd or even.
d. Any real number x can be written as a fraction.
Write the statements from above using the logical quantifiers ∀ and ∃ .
Negate the statements from above (first question) using the logical quantifiers ∀ and ∃ .
a. There exist real numbers a and b such (a+b)^2 = a^2 + b^2.
b. For any real number x, there exists a unique number -x such that x + (-x) = 0.
c. Any integer n is either odd or even.
d. Any real number x can be written as a fraction.
Write the statements from above using the logical quantifiers ∀ and ∃ .
Negate the statements from above (first question) using the logical quantifiers ∀ and ∃ .
Answers
Answered by
Steve
(a) true: a=0 or b=0
∃ a,b ∊ R : (a+b)^2 = a^2+b^2
(b) true
(c) true
(d) false
∃ a,b ∊ R : (a+b)^2 = a^2+b^2
(b) true
(c) true
(d) false
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