Without using any examples explain the difference between eq

Without using any examples, explain the difference between equal and equivalent b) Without using any examples, explain the difference between valid and true Rewrite each statement below into an equivalent statement using If- Then form a) It rains whenever the wind blows from the northeast b) It is necessary to have a valid password to log on to the Discrete Math course site. c) I will remember to send you the address only if you send me an email first. d) A sufficient condition for the warranty to be valid is that you bought the computer less than a year ago. e) Knowing f(x) is a continuous on [a, b] is sufficient to conclude there is at least one a

Solution

Anwer:-1(a):- When two things are said to be equal, then they are similar in all aspects.

When two things are said to be equivalent, then they are similar in a particular aspect.

According to set theory:- When two sets are said to be equal, then they contain same number of elements.

When two sets are said to be equivalent, then those two sets contain equal number of elements.

Answer for 1b):- TRuth and Validity are two different notations.

Truth is predicated of propositions , where as validity is predicated of arguments.

Truth is concerned with what is the case.Validity is concerned with whether conclusions follows from premises.Validity is independent of truth.

2a) If the wind blows from the northeast, then it rains

2b) If you have a valid password, then you log on to the discrete math course site.

2c) If you send me an email first,then I will remember to send you the address.

2d) If you bought the computer less than a year ago, then the sufficient condition for the warranty is to be valid.

2e) If f(x) is continuous on [a,b], then thereexist atleast one a<x<b, such that f(x)=0 when f(a)and f(b) have opposite signs.

Inverse of 2a) :- If wind does not blows from the northeast, then it doesnot rain.

Converse of 2d:- If you bought the computer less than a year ago, then the sufficient condition for the warranty to be valid.

Negation of 2e) :- Knowing f(x) is discontinuous on [a,b] is sufficient to conclude there is atleast one a<x<b, such that f(x)=0 when f(a) and f(b) have opposite signs.