Question

Найдите AUB, AnB, A\B, B\А, если: a) A={-2,-5, 3, 7, 9}, B={-5, 3, 7, 9}; 6) A= (a, b, m, n}, B = {b, c, d, m, n, t}: B) A={x|xe Z, |x| 2}; r) A=N, B=Z.

Answer 1

а

$A \cup B = \{-2,-5,3,7,9\}\\A \cap B = \{-5,3,7,9 \}\\A - B = \{-2\}\\B - A = \{\}$

б

$A \cup B = \{a,b,c,d,m,n,t\}\\A \cap B = \{b,m,n\}\\A \symbol{92} B = \{a\}\\B \symbol{92} A = \{c,d,t\}$

в

Так как множество B не определено в условии:

$B = \{\}\\A \cup B = A\\A \cap B = \{\}\\A-B=A\\B-A=\{\}$

г

$A \cup B = Z\\A \cap B = N\\A - B = \{\} \\B - A = \{ x, x \in Z, x \leq 0\}$

Answer 2

a) A = {-2, -5, 3, 7, 9}, B = {-5, 3, 7, 9}

a) AUB (union of A and B) = {-2, -5, 3, 7, 9} Explanation: The union of two sets A and B includes all the elements from both sets without repetition.

b) AnB (intersection of A and B) = {-5, 3, 7, 9} Explanation: The intersection of two sets A and B includes the elements that are common to both sets.

c) A\B (set difference of A and B) = {-2} Explanation: The set difference of A and B includes the elements that are in A but not in B.

d) B\A (set difference of B and A) = {} Explanation: The set difference of B and A includes the elements that are in B but not in A. In this case, there are no such elements.

6. A = {a, b, m, n}, B = {b, c, d, m, n, t}

a) AUB (union of A and B) = {a, b, c, d, m, n, t} Explanation: The union of two sets A and B includes all the elements from both sets without repetition.

b) AnB (intersection of A and B) = {b, m, n} Explanation: The intersection of two sets A and B includes the elements that are common to both sets.

c) A\B (set difference of A and B) = {a} Explanation: The set difference of A and B includes the elements that are in A but not in B.

d) B\A (set difference of B and A) = {c, d, t} Explanation: The set difference of B and A includes the elements that are in B but not in A.

r) A = N (the set of natural numbers), B = Z (the set of integers)

a) AUB (union of A and B) = Z (the set of integers) Explanation: The union of the set of natural numbers and the set of integers includes all the elements from both sets.

b) AnB (intersection of A and B) = N (the set of natural numbers) Explanation: The intersection of the set of natural numbers and the set of integers includes only the elements that are common to both sets, which in this case is the set of natural numbers.

c) A\B (set difference of A and B) = {} Explanation: The set difference of the set of natural numbers and the set of integers includes the elements that are in A but not in B. In this case, there are no such elements.

d) B\A (set difference of B and A) = Z \ N (the set of integers excluding the natural numbers) Explanation: The set difference of the set of integers and the set of natural numbers includes the elements that are in B but not in A, which in this case is the set of integers excluding the natural numbers.