Theory of Computation Exercise 1 Set

1. แบบฝกหัดที่ 1 เซ็ต
1. ใหนิสิตพิจารณาขอตอไปนี้วา ผิด หรือ ถูก
1.1. กําหนดให 𝐴 = {1,2,3,4}
........... 1) 1 ∈ 𝐴
........... 2) 3 ∈ 𝐴
........... 3) 2,3 ∉ 𝐴
........... 4) 3,4 ∉ 𝐴
1.2. กําหนดให 𝐴 = {1, 1, 2 , 2,3, {}, {∅}}
........... 1) 1,2 ∈ 𝐵
........... 2) {∅} ∈ 𝐵
........... 3) ∅ ∈ 𝐵
........... 4) { 1,2 , 2,3} ∈ 𝐵
1.3. กําหนดให 𝐴 = {𝑥 ∈ ℤ! | − 5 ≤ 𝑥 < 4}
........... 1) −5 ∈ 𝐴
........... 2) 0 ∈ 𝐴
........... 3) {−5, −2,3} ∈ 𝐴
........... 4) 3 ∉ 𝐴
2. กําหนดให 𝐴 = 0,1 , 𝐵 = −1,0,1 , 𝐶 = −1, {0,1},2 และ 𝐷 = 1,2
ใหนิสิตพิจารณาขอตอไปนี้วา ผิด หรือ ถูก
........... 1) 0 ∈ 𝐴
........... 2) {0} ⊂ 𝐴
........... 3) {1,2} ∈ 𝐵
........... 4) {0,1} ⊂ 𝐵
........... 5) {0,1} ∈ 𝐶
........... 6) {0,1} ⊂ 𝐶
........... 7) 0 ∈ 𝐶
........... 8) {0} ∈ 𝐶
........... 9) {−1,0,1} ∈ 𝐵
........... 10) 𝐴 ⊂ 𝐵
........... 11) 𝐷 ⊂ 𝐶
........... 12) 𝐴 ∈ 𝐶
........... 13) 𝐴 ⊂ 𝐶
........... 14) 𝐵 ∈ 𝐶
........... 15 𝐵 ⊂ 𝐶
........... 16) ∅ ⊂ 𝐴
........... 17) ∅ ∈ ∅
........... 18) ∅ ⊂ ∅
........... 19) ∅ ⊂ {−1,2}
........... 20) ∅ ⊂ {∅}
ชื่อ-นามสกุล ...................................................................................... รหัสประจําตัว ........................... หมูเรียน ..........

2. 3. จงหาเพาเวอรเซตของเซตตอไปนี้
3.1. 𝐴 = {1}
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3.2. 𝐵 = {𝑎, 𝑏}
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3.3. 𝐶 = {1, {3,5}}
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3.4. 𝐷 = {{1, 3,5 }}
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3.5. 𝐸 = {{𝑎}}
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3.6. 𝐹 = {∅}
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3.7. 𝐹 = {∅, 1}
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3.8. 𝐺 = {−1,2}
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3.9. 𝐻 = {−1, ∅, 1}
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ชื่อ-นามสกุล ...................................................................................... รหัสประจําตัว ........................... หมูเรียน ..........

3. 4. จงหาสับเซตของเซตตอไปนี้
4.1. 𝐴 = {2,4}
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4.2. 𝐵 = {𝑎, 𝑏, 𝑐}
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4.3. 𝐶 = {1, {3,5}}
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4.4. 𝐷 = {1, ∅}
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4.5. 𝐸 = { 2 , 3, {∅}}
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4.6. 𝐹 = { 2 , {3}}
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4.7. 𝐺 = { 2 , 3 ∅ }
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ชื่อ-นามสกุล ...................................................................................... รหัสประจําตัว ........................... หมูเรียน ..........

4. 5. จงหาจํานวนสับเซตของเซตตอไปนี้
5.1. 𝐴 = {2,4}
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5.2. 𝐵 = {𝑎, 𝑏, 𝑐}
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5.3. 𝐶 = {1, {3,5}}
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5.4. 𝐷 = {1, ∅}
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5.5. 𝐸 = { 2 , 3, {∅}}
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5.6. 𝐹 = { 2 , {3}}
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5.7. 𝐺 = { 2 , 3 ∅ }
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ชื่อ-นามสกุล ...................................................................................... รหัสประจําตัว ........................... หมูเรียน ..........

5. 6. กําหนดให
𝕌 = {0,1,2,3,4,5,6,7,8,9}
𝐴 = {0,2,4,6,8}
𝐵 = 1,3,5,87,9
𝐶 = {2,3,5,7}
จงแจกแจงสมาชิกชองเซตตอไปนี้
6.1. 𝕌⋂A
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6.2. B⋂A
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6.3. A⋂C
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6.4. B⋂C⋂A
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6.5. 𝕌⋃A
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6.6. B⋃A
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6.7. A⋃C
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6.8. B⋃C⋃A
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6.9. A′
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ชื่อ-นามสกุล ...................................................................................... รหัสประจําตัว ........................... หมูเรียน ..........

6. 7. กําหนดให
𝕌 = 𝑥 𝑥 ∈ ℤ! }
𝐴 = {𝑥 ∈ ℤ! |5 < 𝑥 < 10}
𝐵 = 𝑥 ∈ ℤ! |2 ≤ 𝑥 < 8
𝐶 = 𝑥 ∈ ℤ! |6 < 𝑥 ≤ 12
จงแจกแจงสมาชิกชองเซตตอไปนี้
7.1. 𝕌⋂A
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7.2. B⋂B
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7.3. A⋂B
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7.4. A⋂B⋂C
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7.5. 𝕌⋃A
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7.6. B⋃C
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7.7. A⋃C
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7.8. B⋃C⋃A
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7.9. B′
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ชื่อ-นามสกุล ...................................................................................... รหัสประจําตัว ........................... หมูเรียน ..........

7. 8. กําหนดให
𝕌 = {0,1,2,3,4,5,6,7,8,9}
𝐴 = {0,2,4,6,8}
𝐵 = 1,3,5,87,9
𝐶 = {2,3,5,7}
จงแจกแจงสมาชิกชองเซตตอไปนี้
8.1. 𝕌′
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8.2. B′
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8.3. B′⋂C
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8.4. (A⋃C)′
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8.5. B⋃C′
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8.6. B − C
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8.7. A − C
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8.8. B⋃C − A
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8.9. 𝕌 − A
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ชื่อ-นามสกุล ...................................................................................... รหัสประจําตัว ........................... หมูเรียน ..........

8. 9. กําหนดให
𝕌 = 𝑥 𝑥 ∈ ℤ! }
𝐴 = {𝑥 ∈ ℤ! |5 < 𝑥 < 10}
𝐵 = 𝑥 ∈ ℤ! |2 ≤ 𝑥 < 8
𝐶 = 𝑥 ∈ ℤ! |6 < 𝑥 ≤ 12
จงแจกแจงสมาชิกชองเซตตอไปนี้
9.1. 𝕌′
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9.2. B′
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9.3. B′⋂C
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9.4. (A⋃C)′
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9.5. B⋃C′
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9.6. B − C
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9.7. A − C
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9.8. B⋃C − A
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9.9. 𝕌 − A
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ชื่อ-นามสกุล ...................................................................................... รหัสประจําตัว ........................... หมูเรียน ..........

9. 10. จงเขียนแผนภาพแสดงความสัมพันธของสมาชิกเซตเหลานี้
1. A⋃B′
2. (A⋃B)′
3. A′⋂B
4. (A⋂B)′
5. A′⋃B′⋃C′
6. (A⋂B⋂C)′
7. A′⋂B′⋂C′
8.
B⋂A − C
ชื่อ-นามสกุล ...................................................................................... รหัสประจําตัว ........................... หมูเรียน ..........