1 What are the two conditional statements that form the bioo

1. What are the two conditional statements that form the bioonditional given below. An integer s dvisble by 100 if and only if its last two digits are zeros I. An integer is divisible by 100 Il. An integer\'s last two digits are zeros if and only if it is divisble by 100 III. IH an integer\'s last two digits are zeros, then it is divisible by 100 IV. An insegers last two digits are zeros v. an integer is divisible by 100, then its last two digits are zeros. Vi. An inbeger is divisible by 100 if and only fits last two digits are zeros A land IV only B. land V only C. ll and VI only D. All of the above 2. What are the two conditional statements that form the biconditional given below A polygon is a triangle if and only if it has exactly three sides I. A polygon is a triangle if and only fit has exactly three sides Il. A polygon has exactly three sides if and only if it is a triangle IIL. If a polygon is a triangle, then it has exacty three sides. IV. If a polygon has exactly three sides, then it is a triangle V. A polygon has exactly three sides. M. A polygon is a triangle A 1andll only B. V and VM only C land IV only D. Al of the above 3. Test the statement below to see if it is reversible. If so, write it as a true biconditional A quadrilateral has exactly four sides A The statement is not reversible. B. A figune is a quadriateral & and only if the Sgure has exacty four sides C. A figure is a quadrilateral fthe figure has exactly four sides D. If a figure has exactly four sides, then it is a quadeilateral. 4. Use the conditional statement shown below, State the converse. If a number is divisible by 10, then it is divisble by 5 A Ha number is divisible by 5, then the number is not divisible by 10 B. a number is not divisible by 10, then t is not divisble by 5 C Ia number is not divisible by 5, then it is not divisible by 10 D. a number is divisible by 5, then it is divisible by 10 5. Use the true conditional statement shown below, State the converse. If a number is negative, then ts square is positive. A the square of a number is postive, then the number is negative B. Ha number is not negative, then Es square is not positive C If the square of a number is not positive, then the number is not negative D. the square of a number is positive, then the number is not negative 6. Use the statement below and ts converse to write a biconditional. a polygon has exactly three sides, then is a triange A A polygon is a triangle if and only id it has exactly three sides B. Ifa polygon is a triangle, then it has exactly three sides C. A polygon is not a triangle if and only if it does not have exacty three sides D. A polygon does not have exactly three sides if and only if it is a briangle

Solution

1. B

2. C

3.D

4.D (Although it is not correct mathematically, but it is not necessary for converse to be true)

Note:  a proposition may be true but have a false converse.

5.A

6.B