Question

1) Are the following statements true or false
a) If a whole number less than 10 is odd, then it must be a factor of 10
b) A whole number less than 10 that is a factor of 10 must be odd
2)Are the following statements always, sometimes, or never true? Explain
a) A whole number that is even and less than 10 is a factor of 6
b) A factor of 6 that is less than 10 is even

Answer 1

Okay now first let's see the odd numbers between 1 and 10. The odd numbers are 1,3,5,7,9 . The even numbers are 2,4,6,8,10. The factors of 10 are 1,2,5 and 10. The factors of 6 are 1,2,3,6. Now let's just apply this info to your questions . (A) says that a whole number less than 10 if odd must be a factor of 10 which is clearly FALSE coz 3 is an odd number less than 10 but is it a factor ?! Nope !! Next , (B) says that a whole number less than 10 , if a factor of 10 must be odd. This is also FALSE because 2 is a factor of 10 but it is EVEN !! 2A says that a whole number less than 10 and if even is a factor of 6 -- FALSE because 4 is less than 10 and is even but isn't a factor !! Now a factor of 6 less than 10 is even --- FALSE coz 1 is also a factor of 6 but it's odd !!

Answer 2

Q1.
a) this is false as there are certain odd numbers like 3,7,9 which are less than 10 and odd but not the factor of 10.

b)no, it is not necessary as 2 is also a factor of 10 and a whole number but not a odd number.

Q2.

a)this is some times true, as number 2 is a whole even number less than 10 and a factor of 6 but we can't say that 4 is a factor of 6 inspite of being whole even number less than 10.

b)this is also sometimes true as in case of 2 it is even factor of six and less than 10 but 3 is not even inspite of being factor of 6 and less than 10.