Logic and reasoning in math

Question

Read the argument below. Then answer the question?

 

 .

If a shape is a parallelogram, then the shape has four sides.

If a shape has four sides, then it is a quadrilateral.

 

Therefore, if a shape is a parallelogram, then it is a quadrilateral.

 

A.  Is this a valid argument?

 

B.  Explain why or why not.

Answer 1

Let...p=a shape is a parallalogram

      q= a shape has 4 sides

      r= a shape is a quadrilateral

The urgument in symbolic form

  =(p→q),(q→r),(p→r)

={(p→q)^(q→r)^p}→r

truth table

p	q	r	p→q (a)	q→r (b)	a^b	a^b^p	(a^b^p)→r
T	T	T	T	T	T	T	T
T	T	F	T	F	F	F	T
T	F	T	F	T	F	F	T
T	F	F	F	T	F	F	T
F	T	T	T	T	T	F	T
F	T	F	T	F	F	F	T
F	F	T	T	T	T	F	T
F	F	F	T	T	T	F	T

                      (i)                      (ii)                  (iii)          (iv)                 (v)

(a) the urgument is valid

(b) it is valid since its a tautology{all truth values in column (v) are true} and its premises imply the conclusion