Appendix 1: Proofs in Mathematics | A1.2

Question 1

Given that all women are mortal, and suppose that A is a woman, what can we conclude about A?

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Solution

We will use the given statements to find a logical conclusion.

Step 1 — Understand the general rule

We are given a general statement. This statement tells us about all women. It says that all women are mortal.

Diagram 1

Step 2 — Understand the specific case

We are also given a specific fact. This fact is about a person named A. It states that A is a woman.

Diagram 2

Step 3 — Form the conclusion

Person A is part of the group "women". We know all "women" are "mortal". So, A must also be mortal.

A is mortal\boxed{\text{A is mortal}}

Answer

(i) A is mortal.

More questions in A1.2

Q1

Given that all women are mortal, and suppose that A is a woman, what can we conclude about A?

Q2

Given that the product of two rational numbers is rational, and suppose aa and bb are rationals, what can you conclude about abab?

Q3

Given that the decimal expansion of irrational numbers is non-terminating, non-recurring, and 17\sqrt{17} is irrational, what can we conclude about the decimal expansion of 17\sqrt{17}?

Q4

Given that y=x2+6y = x^2 + 6 and x=1x = -1, what can we conclude about the value of yy?

Q5

Given that ABCD is a parallelogram and B=80\angle B = 80^\circ. What can you conclude about the other angles of the parallelogram?

Q6

Given that PQRS is a cyclic quadrilateral and also its diagonals bisect each other. What can you conclude about the quadrilateral?

Q7

Given that p\sqrt{p} is irrational for all primes pp and also suppose that 3721 is a prime. Can you conclude that 3721\sqrt{3721} is an irrational number? Is your conclusion correct? Why or why not?

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