并集bìngjí

Khai niem co ban

Hop cua hai tap hop A va B, ky hieu A ∪ B, la tap hop chua tat ca cac phan tu thuoc A hoac B (hoac ca hai).

Dinh nghia toan hoc

$A \cup B = \{x | x \in A \text{ hoac } x \in B\}$

Mot phan tu thuoc hop khi no thuoc it nhat mot trong hai tap hop.

Tinh chat quan trong

1. Tinh giao hoan

$A \cup B = B \cup A$

2. Tinh ket hop

$(A \cup B) \cup C = A \cup (B \cup C)$

3. Phan tu don vi

$A \cup \emptyset = A$ (tap rong la phan tu don vi)

4. Tinh luy dang

$A \cup A = A$

5. Hop voi tap vu tru

$A \cup U = U$ (U la tap hop vu tru)

Cong thuc so phan tu

$|A \cup B| = |A| + |B| - |A \cap B|$

Cong thuc nay dam bao cac phan tu chung khong bi dem hai lan.

Vi du

Vi du 1: Tap hop huu han

Cho: A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}

Tim: A ∪ B

Giai: Tat ca phan tu tu ca hai tap hop: 1, 2, 3, 4, 5, 6, 7

Dap an: A ∪ B = {1, 2, 3, 4, 5, 6, 7}

Vi du 2: Hop cua khoang

Cho: A = [-2, 3], B = [1, 5]

Tim: A ∪ B

Giai: Hop cua hai khoang la [-2, 5]

Dap an: A ∪ B = [-2, 5]

Bai tap CSCA

Vi du 1: Co ban (Do kho ★☆☆☆☆)

Neu A = {a, b, c, d} va B = {c, d, e, f}, tim A ∪ B.

Giai: Tat ca phan tu: a, b, c, d, e, f

Dap an: {a, b, c, d, e, f}

Vi du 2: Trung binh (Do kho ★★★☆☆)

Neu |A| = 5, |B| = 4 va |A ∩ B| = 2, tim |A ∪ B|.

Giai: $|A \cup B| = |A| + |B| - |A \cap B| = 5 + 4 - 2 = 7$

Dap an: 7

Vi du 3: Nang cao (Do kho ★★★★☆)

Neu A ∪ B = A, moi quan he giua tap hop A va B la gi?

Giai: Neu A ∪ B = A, thi moi phan tu cua B cung phai thuoc A.

Dap an: B ⊆ A (B la tap con cua A)

Loi thuong gap

Loi 1: Nham lan hop va giao

Sai: A ∪ B chi bao gom phan tu chung

Dung: A ∪ B bao gom tat ca phan tu tu ca hai tap hop

Loi 2: Dem trung so phan tu

Sai: |A ∪ B| = |A| + |B|

Dung: |A ∪ B| = |A| + |B| - |A ∩ B|

Meo hoc tap

1. Tu duy "HOAC": Hop co nghia la HOAC - phan tu phai thuoc IT NHAT MOT tap hop
2. Ve bieu do Venn: Bieu dien truc quan giup tranh sai sot
3. Nho cong thuc so phan tu: Luon tru giao!

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Meo thi: Cho bai toan so phan tu, luon su dung cong thuc |A ∪ B| = |A| + |B| - |A ∩ B|!