Assalamualaikum wr wb THE DEFINITION OF A STATEMENT

Assalamu’alaikum wr. wb THE DEFINITION OF A STATEMENT, OPEN SENTENCES, AND NEGATION OF A STATEMENT

WHAT THE MEANING OF A STAREMENT… ?

1. THE DEFINITON OF A STATEMENT A statement is a sentence which has logical value (truthfulness) true of false, but not both true and false at the same time. in other words, a statement is a sentence which truth value can be determined, which are true or false. The following are examples of statements and their truth values. a. A squere plane has four cornes. (True) b. The value of X which complies with 2 X = 10 is 6 (false) it is important to know that every statement is a sentence but not every sentence is a statement. because not statement their truth value cannot or cannot yet be determined.

For examples : Determine truth values of this statement…! 1. Watch your brother ! 2. the sun rises in the east.

Solutions a. Not a statement, because is impertive sentence. b. A statement, because a sentence which has logical values.

WHAT THE MEANING OF A OPEN SENTENCE…?

2. THE DEFINITON OF A OPEN SENTENSE A open sentence is a sentence which truth value cannott yet be determined because it still contains variable is a symbol which represents any members of a universe of discourse. An open statement can change into a statement if is changed with a constant, which is a symbol which represents a specific member of a universe of discourse.

For Example : Determine the solution set of the following open statement if X are variables of whole numbers. 3 X + 6 = 5 X - 4

SOLUTIONS 3 X + 6 = 5 X – 4 3 X – 5 X =-4 – 6 -2 X = -10 X=5 Therefore, the solution set is (5)

3. THE DEFINITON OF NEGATION OF A STATEMENT…?

3. THE DEFINITON OF NEGATION OF A STATEMENT A negation of a statement is a new statement which truth value is true if the original statement’s truth value is false or its truth value is false if the original statement’s truth value is true.

For Examples : Determine negations of the statement. A. A sguare plane has level one folding symmetry (S) B. 5 + 6 ≠ 6(B)

Solution A. it is not true that a square plane has level one folding symmetry (B) B. 5 + 4 = 6 (S)

Conclusion A statement is a sentence which has logical value (truthfulness) true of false, but not both true and false at the same time. in other words, a statement is a sentence which truth value can be determined, , which are true or false. A open sentence is a sentence which truth value cannott yet be determined because it still contains variable is a symbol which represents any members of a universe of discourse. A negation of a statement is a new statement which truth value is true if the original statement’s truth value is false or its truth value is false if the original statement’s truth value is true.