TMUA · Paper 2: Mathematical Reasoning

Valid and invalid arguments

6 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 6 questions

Which of the following arguments is valid?
Which of the following arguments is invalid?
A student argues: 'All prime numbers greater than 2 are odd. The number 15 is odd. Therefore 15 is prime.' What is wrong with this argument?
It is given that if $f^{'} (x) > 0$ for all $x$ in $(a, b)$ , then $f$ has no stationary point in $(a, b)$ . A student concludes: *' $f$ has no stationary point in $(a, b)$ , so $f^{'} (x) > 0$ for all $x$ in…
A student argues: 'If a triangle is equilateral then it is isosceles. This triangle is not equilateral. Therefore it is not isosceles.' What is wrong with this argument?
A student solves $x^{2} - 3 x = 4$ as follows: *'Factorising, $x (x - 3) = 4$ . So $x = 4$ or $x - 3 = 4$ , giving $x = 4$ or $x = 7$ .'* What is wrong with this argument?

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