For the given statement below, “ For any two integers a and b, if both ab and a+b are even, then both a and b are even.” Do the following three things (Assume that E represents the even number set and O represents the odd number set) : Translate the following statement into a symbolic logic form Negate the logic form you came up with from step a), and simplify the negated form as much as you can. Give the contraposition of the logic form from step a), and translate the contraposition back to plain English (Hint: No need to change the quantifiers if any. Why?).
Operations
In mathematics and computer science, an operation is an event that is carried out to satisfy a given task. Basic operations of a computer system are input, processing, output, storage, and control.
Basic Operators
An operator is a symbol that indicates an operation to be performed. We are familiar with operators in mathematics; operators used in computer programming are—in many ways—similar to mathematical operators.
Division Operator
We all learnt about division—and the division operator—in school. You probably know of both these symbols as representing division:
Modulus Operator
Modulus can be represented either as (mod or modulo) in computing operation. Modulus comes under arithmetic operations. Any number or variable which produces absolute value is modulus functionality. Magnitude of any function is totally changed by modulo operator as it changes even negative value to positive.
Operators
In the realm of programming, operators refer to the symbols that perform some function. They are tasked with instructing the compiler on the type of action that needs to be performed on the values passed as operands. Operators can be used in mathematical formulas and equations. In programming languages like Python, C, and Java, a variety of operators are defined.
For the given statement below,
“ For any two integers a and b, if both ab and a+b are even, then both a and b are even.”
Do the following three things (Assume that E represents the even number set and O represents the odd number set) :
- Translate the following statement into a symbolic logic form
- Negate the logic form you came up with from step a), and simplify the negated form as much as you can.
- Give the contraposition of the logic form from step a), and translate the contraposition back to plain English (Hint: No need to change the quantifiers if any. Why?).
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