Sample example of follow expressions. Logic OR \[T(a,b)=a\vee b\]
>> $T = a+b >> $T +----------+-----+ | a b | R | +----------+-----+ | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 1 | +----------+-----+
Upper case letter are negate \[T(a,b)=a\vee (\neg b)\]
>> $T=a+B >> $T +----------+-----+ | a b | R | +----------+-----+ | 0 0 | 1 | | 0 1 | 0 | | 1 0 | 1 | | 1 1 | 1 | +----------+-----+
If, only If \[T(a,b)= a\iff b\]
>> $T=a<->b >> $T +----------+-----+ | a b | R | +----------+-----+ | 0 0 | 1 | | 0 1 | 0 | | 1 0 | 0 | | 1 1 | 1 | +----------+-----+
Negating \[T(a,b,c,d)=\neg(a\wedge b \wedge c\wedge (\neg d))\]
>> $T=!(abcD) >> $T +--------------------+-----+ | a b c d | R | +--------------------+-----+ | 0 0 0 0 | 1 | | 0 0 0 1 | 1 | | 0 0 1 0 | 1 | | 0 0 1 1 | 1 | | 0 1 0 0 | 1 | | 0 1 0 1 | 1 | | 0 1 1 0 | 1 | | 0 1 1 1 | 1 | | 1 0 0 0 | 1 | | 1 0 0 1 | 1 | | 1 0 1 0 | 1 | | 1 0 1 1 | 1 | | 1 1 0 0 | 1 | | 1 1 0 1 | 1 | | 1 1 1 0 | 0 | | 1 1 1 1 | 1 | +--------------------+-----+
Evaluating a expression \[T(a,b,c)=a\wedge b \vee (\neg c)\] \[T(1,1,0)\]
>> $T=ab+C >> $T[1,1,0] 1
Using logic AND \[T(a,b,c)=(a\vee b)\wedge c\]
>> $T=(a+b)c >> $T +---------------+-----+ | a b c | R | +---------------+-----+ | 0 0 0 | 0 | | 0 0 1 | 0 | | 0 1 0 | 0 | | 0 1 1 | 1 | | 1 0 0 | 0 | | 1 0 1 | 1 | | 1 1 0 | 0 | | 1 1 1 | 1 | +---------------+-----+
Using implication \[T(a,b)=a \to b\]
>> $T=a->b >> $T +----------+-----+ | a b | R | +----------+-----+ | 0 0 | 1 | | 0 1 | 1 | | 1 0 | 0 | | 1 1 | 1 | +----------+-----+
Using XOR \[T(a,b)=a \oplus b\]
>> $T=a^b >> $T +----------+-----+ | a b | R | +----------+-----+ | 0 0 | 0 | | 0 1 | 1 | | 1 0 | 1 | | 1 1 | 0 | +----------+-----+
Chang logic symbols (1, 0) to (T, F) \[T(a,b)=(\neg a) \wedge (\neg b)\]
>> $T=AB >> setlogic[T,F] >> $T +----------+-----+ | a b | R | +----------+-----+ | F F | T | | F T | F | | T F | F | | T T | F | +----------+-----+
Compare expressions \[A(a,b)=(\neg a)\wedge(\neg b)\] \[B(a,b)=\neg( a\vee b)\]
>> setlogic[T,F] >> $A=AB >> $B=!(a+b) >> $A == $B T