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A few examples are given below.
Example 1: Draw the truth table for the Boolean expression A'.B + A.B'
A B A'.B A.B' A'.B + A.B'
Solution: The above expression has two variables A and B. So, there
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will be 2 , i.e., 4 input combinations. The first column representing A in 0 0 0 0 0
this expression will follow the order as ‘First two 0’s followed by two 0 1 1 0 1
1’s’. The second column representing B will have alternate 0 and 1 1 0 0 1 1
repeated twice. 1 1 0 0 0
A B C A.B B.C A.B + B.C
Example 2: Draw the truth table for the Boolean expression 0 0 0 0 0 0
A.B + B.C
0 0 1 0 0 0
Solution: The above expression has 3 variables A, B and C. So 0 1 0 0 0 0
there will be 2 , i.e., 8 input combinations. The first column 0 1 1 0 1 1
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representing A in this expression will store the first four 0’s and 1 0 0 0 0 0
then the next four 1’s. The middle column containing B will 1 0 1 0 0 0
have two 0’s then two 1’s and then again two 0’s and two 1’s. 1 1 0 1 1 1
The last column representing C has alternate 0 and 1 repeated 1 1 1 1 1 1
four times.
A B C D A.B B.C.D A.B + B.C.D
Example 3: Draw the truth table for the Boolean 0 0 0 0 0 0 0
expression A.B + B.C.D 0 0 0 1 0 0 0
Solution: The above expression has 4 variables A, B, 0 0 1 0 0 0 0
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C and D. Total input combinations will be 2 , i.e., 16. 0 0 1 1 0 0 0
The first column representing A in this expression 0 1 0 0 0 0 0
will store the first eight 0’s and the next eight 1’s. 0 1 0 1 0 0 0
The second column representing B will have four 0’s 0 1 1 0 0 0 0
followed by four 1’s repeated twice. The third column 0 1 1 1 0 1 1
representing C has two 0’s and two 1’s repeated four 1 0 0 0 0 0 0
times. The last column representing D has alternate 0 1 0 0 1 0 0 0
and 1 written eight times. 1 0 1 0 0 0 0
1 0 1 1 0 0 0
1 1 0 0 1 0 1
1 1 0 1 1 0 1
1 1 1 0 1 0 1
1 1 1 1 1 1 1
1.3 SYMBOLS OR CONNECTIVES
Connectives or logical operators are the symbols that join two or more simple propositions to form compound
propositions. There are mainly five connectives which are discussed in the following sub-sections.
1.3.1 Negation (NOT)
Negation inverts a single statement. It is also called a unary connective. If a proposition is true, then negation makes it
̅
false and vice-versa. It is represented by a tilde sign (∼), an apostrophe (') or a bar sign ( ).
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Boolean Algebra 15

