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MAT 3702 Assignment 1 2026
Due Date: 13 May 2026
1. Let A, B, C be sets and show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
Question 1
Let
.
Then
or
.
(⊆) x ∈ A ∪ (B ∩ C)
x ∈ A x ∈ B ∩ C
If
x ∈ A
, then
x ∈ A ∪ B
and
x ∈ A ∪ C
. Hence
x ∈ (A ∪ B) ∩ (A ∪ C)
.
If
x ∈ B ∩ C
, then
x ∈ B
and
x ∈ C
. Hence
x ∈ A ∪ B
and
x ∈ A ∪ C x ∈ (A ∪ B) ∩
, so
MAT 3702 Assignment 1 2026
Due Date: 13 May 2026
1. Let A, B, C be sets and show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
Question 1
Let
.
Then
or
.
(⊆) x ∈ A ∪ (B ∩ C)
x ∈ A x ∈ B ∩ C
If
x ∈ A
, then
x ∈ A ∪ B
and
x ∈ A ∪ C
. Hence
x ∈ (A ∪ B) ∩ (A ∪ C)
.
If
x ∈ B ∩ C
, then
x ∈ B
and
x ∈ C
. Hence
x ∈ A ∪ B
and
x ∈ A ∪ C x ∈ (A ∪ B) ∩
, so
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MAT 3702 Assignment 1 2026
Due Date: 13 May 2026
1. Let A, B, C be sets and show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
Question 1
Let
.
Then
or
.
(⊆) x ∈ A ∪ (B ∩ C)
x ∈ A x ∈ B ∩ C
If
x ∈ A
, then
x ∈ A ∪ B
and
x ∈ A ∪ C
. Hence
x ∈ (A ∪ B) ∩ (A ∪ C)
.
If
x ∈ B ∩ C
, then
x ∈ B
and
x ∈ C
. Hence
x ∈ A ∪ B
and
x ∈ A ∪ C x ∈ (A ∪ B) ∩
, so
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