"Is this an open or closed set for given operation?"
a) set of odd whole #s for multiplication
b) set of whole #s less than 100 for addition
c) set of all whole #s whose units digits are 6 for multiplication
a)/c) are closed….b) is open, please explain!
a) When you multiply two odd whole numbers the answer is an odd whole number. That is why the set of odd whole numbers is closed with respect to multiplication.
b) 100 and 1 are both less than 100 but when you add them you get 101 which is not less than 100. That is why the set of whole numbers less than 100 is NOT closed with respect to addition.
c) When you multiply a number that ends in 6 times another number that ends in 6 the answer ends in 6. That is why the set of whole numbers which end in 6 is closed with respect to multiplication.
November 24th, 2009 at 7:36 am
A is open because the set of odd whole numbers for multiplication is infinite, it goes on forever. Same for c, there is no stopping point.
B has two stopping points. Whole numbers tells us the set of counting numbers starting with 0 and then all positive numbers, but in b, it tells us that the set stops at whole numbers less than 100, so that closes the set.
wpf.
References :
November 24th, 2009 at 8:26 am
a) When you multiply two odd whole numbers the answer is an odd whole number. That is why the set of odd whole numbers is closed with respect to multiplication.
b) 100 and 1 are both less than 100 but when you add them you get 101 which is not less than 100. That is why the set of whole numbers less than 100 is NOT closed with respect to addition.
c) When you multiply a number that ends in 6 times another number that ends in 6 the answer ends in 6. That is why the set of whole numbers which end in 6 is closed with respect to multiplication.
References :