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