# Mathematically Acceptable Statements

Introduction

The statement that is proved is often called a theorem. Once a theorem is proved, it can be used as the basis to prove further statements. A theorem may also be referred to as a lemma, especially if it is intended for use as a stepping stone in the proof of another theorem.

## Mathematically acceptable statements types of acceptable statement :

1.  value statement  of a mathematically statement

2. Sentences statements  and their truth sets

3 statements for Quantifiers  and  statement quantified

4. statement of a  negative mathematically

5. statement of a Negation  of a quantified statement

6.  Mathematically  Simple   statements

7  mathematically Compound  statements

8. mathematically Logical  acceptable statements

## Mathematically acceptable statements problems:

1. Write down the Truth value of each of the following statements:

(i)4+3=7 and 6>7.

(ii)5+4>9and5<9

(iii)3+3=6and3>3

(iv)3>5and1>2

Solution:(i) Let p:4+3=7

q:6>7

Then,p`^^` q:4+3=7`eta` and6>7

Here,p is true and q is false,and therefor`e,p ``^^` q is false.

Hence,the given statements is false and so its truth value is F

(ii) Let p:5+4>9

q : 5<9

Then,p`^^` q:5+4>9 and5<9

Here,p is false and q is true,and therefore,p`^^` q is false

Hence,the given statement is false and so its truth value is F.

(iii)  Let p: 3+3=6

q:3>3

Then,p`^^` q : 3+3=6and3>3

Here,p is true and q is true,and therefore,p`^^` q is true

Hence the given statement is true and so its truth value is T

(iv) let p:3>5

q:1>2

Then,p`^^` q:3>5and1>2

Here,p is false and q is false and therefore,p`^^` q is false

Hence,the given statement is false and so its truth value is F

2.Write the truth  value of each of the following

(i)5<7 or8>10

(ii)4+5=8or4+5=9

(iii)(1+i)is a real number or it is a complex number

(iv)Every quadratic equation has one real root or two real roots

Solution:      (i)Let p:5<7

q:8>10

Then,p`vv` q:5<7 or 8>10

Here p is true and q is false,and therefore,p`vv` q is true

Hence,the given statement is true,and its truth value is T

(ii) Let p: 4+5=8

q:4+5=9

Then,p`vv` q:4+5=8or4+5=9

here,p is false and q is true,and therefore,p`vv` q is true.

hence,the given statements is true,and its truth value is T

(iii) Let p:(1+i) is a real number

q:(1+i) is a complex number

Then, p`vv` q:(1+i) is a real number or it is a complex number

Here,p is false and q is true,and therefore,p`vv` q is true

hence,the given statements is true and so its truth value is T

(iv) Let p: Every quadratic equation has one real root

q:Every quadratic equation has two real roots

p`vv` q:Every quadratic equation has one real root or two real roots.

Here,p is false and q is false,and therefore,p`vv` q is false

hence,the given statement is false and so its truth value is F