Three of the most important kinds of sentences in mathematics are universal stat

Question

Three of the most important kinds of sentences in mathematics are universal statements, conditional statements, and existential statements. Match the example to the type of statement.

1. This type of statement says that a certain property is true for all elements in a set.

2. This type of statement says that if one thing is true then some other thing also has to be true.

3. This type of statement says that given a property that may or may not be true, there is at least one thing for which the property is true.

A. All positive numbers are greater than zero.

B. If 378 is divisible by 18, then 378 is divisible by 6.

C. There is a prime number that is even.

Explanation / Answer

Answer

1 ---- A

2 ----- B

3 ---- C

explanation

1 --- A

all +ve no is greater then 0. this statement is true for all +ve element thats 1 is machng with A.

2 ---- B

if a no is divisibel b 18 then it also divisibel by 6 since

let x is divisibel by 18 means there exist a y such that

x= 18 * y   

x= 6 * (3 y.)

thus from able it is clear that statement if x is divisible by 18 is true it imples that x is divisible by 6 also.

thats why 2 --- B.

There is a prime number that is even. it is true for 2. so it matches for 3--C

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