Logical Statements and Quantifiers Notes

Tuesday, February 17, 2026

Logical Statements and Quantifiers Notes

 

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LOGIC GATES' BASIC OPERATION

Friday, February 26, 2016

LOGIC GATES

Logic gates are electronics logical symbols for yes or no with 1 or 0 value respectively. 

Some uses true or false instead of 1 and 0, or for yes or no. The illustration below shows 

the basic of logic gates. All data in computer use binary information in each system. 

The 1 or 0 shows a binary relationship between each other. Its opposite will always be the 

counterpart of each.

Illustration:

For the following operators,AND,OR,and NOT gates, each relationships between inputs for 

A and B has the corresponding result in C as an output.

In Boolean Algebra the "AND" symbol is "ᴧ". Thus we can say "A ᴧ B" for "A and B". And 

For "OR" we use "A V B" or read as "A OR B". We use the symbol " ~ " for not, say "not A" 

we use " ~A". We are always talking binary here. If we negate "0" we mean "1" or 


vice-versa, same as with true or false.



Examples:

Use logic gates to represent the given logic circuits.

1. A ᴧ ~B. In here we need to evaluate the "not" symbol.

Provided photo for the solution

2. A v ~B. Check the "or" symbol.

Provided photo for the solution

3. P v Q. We are allowed to use another letter.

Provided photo for the solution

4. (a ᴧ b) v c

Provided photo for the solution

5. (p v q) ᴧ (r v s)

Provided photo for the solution

Try these as your exercises.

Use logic gates to represent the given logic circuits.

1. (p ᴧ q) v (~r)

2. (p ᴧ q) v (r ᴧ s)

3. (~r ᴧ ~s) ᴧ ~p

4. (a ᴧ b) v (~a ᴧ ~b)

5. ~((~a ᴧ ~b) ᴧ ~c)

6. (~p v q) ᴧ ~(~r ᴧ s)

7. ((p ᴧ q) v (~r)) ᴧ  ((q ᴧ ~p) ᴧ ~p)

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