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Star Operations Solved Problems
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Mathematics
> Star Operations
Which problem do you want to solve ?
If `a ast b = (a^2 - 2b)b`, find:
`3 ast 5`
`r` if `4 ast r = 0`
If `P ast Q` is defined as `4P + Q/2 + 4`. Evaluate `(5 ast -3) ast 3`
Let `ast` be a binary operation on `N` given by `a ast b` = LCM (a,b) for all `a,b in N`. Find `5 ast 7`
If the binary operation `ast` on set `R` of real numbers is defined as `a ast b = (3ab)/7`. Write the identity in `R` for `ast`.
Is the binary operation defined on set `N`, given by :
`a ast b = (a + b)/2` for all `a, b in N`, commutative?
Let `ast` be a binary operation on the set of all non-zero real numbers, given by `a ast b = (ab)/5` for all `a, b in R - {0}`. Find the value of `x` given that: `2 ast (x ast 5) = 10`
Consider the binary operations `ast` `R times R rightarrow R` and `O: R times R rightarrow R` defined as `a ast b = |a - b|` and `aob = a` for all `a, b in RR`. Show that `ast` is commutative but not associative, `o` is associative but not commutative.
Recommended Lessons
Which problem do you want to solve ?
If `a ast b = (a^2 - 2b)b`, find:
`3 ast 5`
`r` if `4 ast r = 0`
If `P ast Q` is defined as `4P + Q/2 + 4`. Evaluate `(5 ast -3) ast 3`
Let `ast` be a binary operation on `N` given by `a ast b` = LCM (a,b) for all `a,b in N`. Find `5 ast 7`
If the binary operation `ast` on set `R` of real numbers is defined as `a ast b = (3ab)/7`. Write the identity in `R` for `ast`.
Is the binary operation defined on set `N`, given by :
`a ast b = (a + b)/2` for all `a, b in N`, commutative?
Let `ast` be a binary operation on the set of all non-zero real numbers, given by `a ast b = (ab)/5` for all `a, b in R - {0}`. Find the value of `x` given that: `2 ast (x ast 5) = 10`
Consider the binary operations `ast` `R times R rightarrow R` and `O: R times R rightarrow R` defined as `a ast b = |a - b|` and `aob = a` for all `a, b in RR`. Show that `ast` is commutative but not associative, `o` is associative but not commutative.
Recommended Lessons