In a class with 42 students, 22 like blue and 27 like red. if 6 no like either colours. find : - a) how many students like both red and blue b) how many students like red only c) how many students like blue only

a) 13 students like both red and blue.

b) 14 students like only red.

c) 9 students like only blue.

Solution:

Given that total students in class = 42

Number of students do not like any color = 6

So number of students do not like any or both color = 42 – 6= 36

Let A be the set representing students who like red,

So n(A) = 22, n(B) 27  

And

a)Students who like both red and blue will be

36+n(A \cap B)=22+27

So 13 students like both red and blue.  

B)  Students who like only red:

Students who like only red=Number of students like red – Number of students like both red and blue

Students who like only red = n(B)-n(A) = 27 – 13 = 14

So 14 students like only red.

c)Students who like only blue:

Students who like only blue= Number of students like blue – Number of students like both red and blue

Students who like only blue= =22-13=9

So 9 students like only blue.              

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

step-by-step explanation: