given u = (all the letters of the alphabets)
x = ( a,e,l,o,u) and
y = (e,b,c,d,f,h)
find (i) x union y
find (ii) x intercept y
find (iii) x'ny'
xUy = {a,b,c,d,f,h,l,o,u}
that is, everything in either set
x∩y is what is in both sets
x'∩y' = (xUy)'
everything except xUy
Please find x union y for me
(i) x union y: Well, that's quite an alphabet soup you have there! The union of x and y would be all the unique letters present in both x and y. So, the union of x and y would be (a, e, l, o, u, b, c, d, f, h).
(ii) x intersect y: Ah, the intersection of x and y. This would be the letters that are present in both x and y. Unfortunately, there seems to be no letter that appears in both x and y. So, the intersection of x and y is an empty set. Guess they're just not meant to be!
(iii) x'ny': This looks like a fun question! x' represents the complement of x, which means all the letters in the alphabet that are not present in x. Similarly, y' represents the complement of y, which means all the letters in the alphabet that are not present in y. So, x'ny' would be the letters that are not in x and not in y. In this case, it would be the remaining letters of the alphabet after excluding the letters in x and y. Boy, those letters must be feeling pretty lonely!
To solve these questions, we will use set operations. Let's break down each question:
(i) x union y:
The union of two sets, denoted by the symbol ∪, represents the combination of all unique elements from both sets. In this case, we need to find all the unique elements present in both set x and set y.
To find the union of x and y, follow these steps:
1. Combine all the elements from set x and set y.
x = {a, e, l, o, u}
y = {e, b, c, d, f, h}
Combine: {a, e, l, o, u, b, c, d, f, h}
2. Remove any duplicate elements.
The resulting set after removing duplicates is {a, e, l, o, u, b, c, d, f, h}.
Therefore, x union y = {a, e, l, o, u, b, c, d, f, h}.
(ii) x intersect y:
The intersection of two sets, denoted by the symbol ∩, represents the common elements present in both sets. In this case, we need to find the common elements between set x and set y.
To find the intersection of x and y, follow these steps:
1. Identify the elements that are present in both set x and set y.
x = {a, e, l, o, u}
y = {e, b, c, d, f, h}
Common elements: {e}
Therefore, x intersect y = {e}.
(iii) x'ny':
To find x'ny', we need to find the complement of set x (denoted by x'), and then the intersection between the complement of x and the set y.
To find x', follow these steps:
1. Identify all the elements that are not present in set x from the universal set (u).
u = {all the letters of the alphabets}
x = {a, e, l, o, u}
Elements not in x from u: {b, c, d, f, g, h, i, j, k, m, n, p, q, r, s, t, v, w, x, y, z}
Now we need to find the intersection between x' and y:
1. x' = {b, c, d, f, g, h, i, j, k, m, n, p, q, r, s, t, v, w, x, y, z}
y = {e, b, c, d, f, h}
Common elements: {b, c, d, f, h}
Therefore, x'ny' = {b, c, d, f, h}.
I hope this helps! Let me know if you have any further questions.