now let's say if we have set a which contain the elements 2 4 5 6 and 9 and we also have set b which contain the elements 2 3 5 6 7 9 and 10. so what is the intersection of set a and b how can we get the answer to find the intersection we need to find out which elements are common to both sets so both sets contain a two they contain a five a six and also a nine so therefore the intersection of sets a and b is two three actually not three but two five six and nine and that's it so that's how you could find the intersection of two sets so now let's work on some more examples you can pause the video and try this one if you want to let me use some different letters so let's say this is set c and it contains the elements 3 4 6 7 and 10 and also set d which contain the elements 3 6 8 and 9. so feel free to pause the video and determine the intersection of sets c and d go ahead and try it so which elements are common to both sets so three is common to both sets six and that's it so for this particular example it's only three and six so that's the intersection of the two sets so this is the answer let's try another example let's say set f contains the elements a b c d f g and j and set g contains the elements a c g h and k so what is the intersection between sets f and g so feel free to take a minute and try so let's see which elements are shared between both sets so both sets contain element a element c g and that is it so the intersection of f and g is going to be a c and g so as you can see finding the intersection is pretty straightforward but now what about this particular example let's say set j contains the elements 5 7 10 and 11 and set k has the elements 2 4 8 and 13. what is the intersection of j and k now notice that there is no common element shared between the two sets the elements in j are completely different from the elements in k so in that case the intersection of j and k is going to be empty there's going to be nothing inside so if there's nothing inside if you have an empty set you have a null set so this is the answer you have to use a greek simplify now let's say we have set r which contains the numbers 3 4 7 and 10 and set s which is basically an empty set what is the intersection of r and s the intersection of a set with numbers and an empty set is going to be another empty set or a null set so that's it for this one now let's focus on the second type of problem that we need to talk about and that is to find the union of two sets so let's say that set a contains the elements one two three and four and set b contains the elements three four five and six so what is the union of these two sets when i think of union i think of combining these into a larger set now notice that we do have some common numbers three and four now the union will contain everything in both sets but 3 and 4 we're not going to write it twice only once so the union of set a and b is going to be 1 2 3 4 5 and 6. so we're going to write everything in both sets but only write it once so let's try some other examples so let's say set c is 3 comma 5 comma 9 11 and 13 and set d is 2 3 6 8 and 12. go ahead and find a union between sets c and d go ahead and try that so all we got to do is just write all the numbers in c and d so let's put it in ascendant order so we have a two a three there's a five a six there's no seven so we have an eight a nine there's no ten but we have an eleven twelve and thirteen and so that's it so that's the union of those two sets here's another example let's say that set j contains the letters a c d and e and that set k contains the letters a b f e and g go ahead and determine the union between j and k so just like before all we need to do is write all the letters so we have an a a b c d e f and g and that's it for that question let's say that set x contains the numbers 2 5 8 12. and set y let's say is an empty set what is the union of a set with numbers and an empty set well the empty set it's not going to add anything it's like saying 15 plus 0 that's going to be 15. so therefore the union of set x with an empty set y is going to be the same as set x this 2 5 8 and 12. it's not going to change but the intersection of a set with something and a set with nothing it's going to be an empty set so just something to keep in mind now here's a question for you let's say if set a contains the numbers 3 4 5 and 7 and set b contains the numbers 2 4 5 and 8. how can you determine the intersection of a and b and a union of a and b and represent the results using a venn diagram so circle a and circle b in its separated form set a contains the numbers 3 4 5 and 7. b contains the numbers 2 4 5 and 8. now the intersection of these two i'm running out of space here is four and five four and five are found in both but to represent that using venn diagrams what we need to do is put the two circles together and draw it this way so this is set a and set b so in the middle is the intersection of a and b which contains these elements 4 and five now a also contains three and seven and b also contains two and eight but four and five is common to a and b so we put that in middle now the union of these two sets is basically everything it contains the numbers 2 3 4 five seven and eight and i'm running out of space so this entire system with the two circles represents the union of a and b because it contains all the numbers 2 3 4 5 7 and 8. but the intersection is limited by this region here because it only contains the elements common to both sets so hopefully this helps you to see the relationship between intersection of sets and union of sets as it relates to venn diagrams so that's it for this video thanks for watching and have a good day you