Question
Which of the following statements are true or false? Give reasons for your answer in the form of a short proof or a counter-example, whichever is appropriate.
a) The set {S ∈R :x2 - 3x + 2 = 0}is an infinite set.
b) The greatest interger function is continuous on R.
c)
d) Every integrable function is monotonic.
e) a⊕b = a + b defines a binary operation on Q, the set of rational numbers.
Answer :
Word Count : 431
Let's go through each statement one by one: ### a) The set \( \{ S \in \mathbb{R} : x^2 - 3x + 2 = 0 \} \) is an infinite set. - False. The equation \( x^2 - 3x + 2 = 0 \) is a quadratic equation that can be factored as \( (x - 1)(x - 2) = 0 \), giving two solutions: \( x = 1 \) and \( x = 2 \). Therefore, the set contains only two elements, which is a ____ _______ ___ ______ __________.
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Let's go through each statement one by one: ### a) The set \( \{ S \in \mathbb{R} : x^2 - 3x + 2 = 0 \} \) is an infinite set. - False. The equation \( x^2 - 3x + 2 = 0 \) is a quadratic equation that can be factored as \( (x - 1)(x - 2) = 0 \), giving two solutions: \( x = 1 \) and \( x = 2 \). Therefore, the set contains only two elements, which is a ____ _______ ___ ______ __________.
____ _______ ________ ________ _____ ______ ____ _______ _____ ________.
__________ __________ ____ _________ _______ _____ ______ ______ ___ ____ ___ __________.
____ __________ ____ ___ _____ ________ ____ ___ ___ ___.
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