Tefko Saracevic, Rutgers University

1

Practice for logical operators

Boolean search statements and

Venn diagrams

Tefko Saracevic, Rutgers University

2

Exact match - Boolean search

• You retrieve exactly what you ask for in the query:– all documents that have the term(s)

with logical connection(s), and possible other restrictions (e.g. to be in titles) as stated in the query

– exactly: nothing less, nothing more

• Based on matching following rules of Boolean algebra, or algebra of sets– ‘new algebra’– presented by circles in Venn diagrams

Tefko Saracevic, Rutgers University

3

Boolean algebra & Venn diagrams

Four basic operations:

1 2 3

A BA alone. All documents that have A. Shade 1 & 2. E.G. apples

1 2 3

A B

A AND B. Shade 2

apples AND oranges

1 2 3

A B

A OR B. Shade 1, 2, 3

apples OR oranges

1 2 3

A B

A NOT B. Shade 1

apples NOT oranges

Tefko Saracevic, Rutgers University

4

Venn diagrams … cont.

Complex statements allowed e.g

12

3

4 5 6

7

A B

C

(A OR B) AND C

Shade 4,5,6

(apples or oranges) AND Florida

(A OR B) NOT C

Shade what?

(apples or oranges NOT Florida

Tefko Saracevic, Rutgers University

5

Directions for exercise

• Slide 7 provides a Venn diagram with numbered sets and a number of search statements– for each statement shade the

appropriate set or sets– e.g. for (A OR B) AND C the sets

are 4, 5, 6

• Slide 8 is for practice

• Slide 9 has the answers– BUT NOTE: one of the answers is

WRONG! Which one?

Tefko Saracevic, Rutgers University

6

Order of operations

• Rules for the order in which operations are done effect the answer - so follow them

• Dialog order of operation is: 1. First are done all operations that are in

parentheses, then:

2. (W), (N), (S), (L), or (F)

3. NOT

4. AND

5. OR• e.g. for A OR B AND C, first is done B

AND C, and then A OR the results of B AND C, thus this is the same as A OR (B AND C)

Tefko Saracevic, Rutgers University

7

Venn diagrams

1 2 3

4 5 6

7

A B

C

1. A AND B

2. A OR B

3. A OR B AND C

4. (A OR B) AND C

5. A AND B NOT C

6. A AND (B NOT C)

7. (A AND B) NOT C

8. (A NOT B) AND C

9. A NOT (B AND C)

10. A NOT B AND C

11. A AND (B OR C)

12. A AND B OR C

13. A OR (B AND C)

14. A OR B OR C

15 A AND B AND C

Tefko Saracevic, Rutgers University

8

12

3

4 5 6

7

A B

C

Use for exercise & shading

Tefko Saracevic, Rutgers University

9

1. A AND B 2,5

2. A OR B 1,2,3,4,5,6

3. A OR B AND C 1,2,4,5,6

4. (A OR B) AND C 4,5,6

5. A AND B NOT C 2

6. A AND (B NOT C) 2

7. (A AND B) NOT C 2

8. (A NOT B) AND C 4

9. A NOT (B AND C) 6

10. A NOT B AND C 4

11. A AND (B OR C) 2,4,5

12. A AND B OR C 2,4,5,6,7

13. A OR (B AND C) 1,2,4,5,6

14. A OR B OR C 1,2,3,4,5,6,7

15 A AND B AND C 5

1 2 3

4 5 6

7

A B

C

Venn diagrams: solutionsp.s. one of them is wrong!