Answer:
Your answer is in of the following questions below in step by step explanation.
Step-by-step explanation:
I. Logic
Are there "rules" or "laws" that govern proper reasoning? Can we prove, mathematically, that a particular argument is valid? To what extent can reasoning be automated?
1. Statement (proposition): a sentence that is either true or false, but not both.
Example. Determine if each of the following sentences is a statement.
a. 5 + 3 = 7
21 / 7 = 3
c. MIDN Miller is President of the United States
d. Ah,…the joy of SM242!
e. He is a midshipman
MIDN Avworo has written C++ programs.
Baltimore is the capital of Maryland.
h. 3 * z < 9
i. Every even integer greater than 2 is the sum of two primes
j. This sentence is false.
2. Compound Statements: a more complex statement composed of simpler statements. The truth-value of a compound statement depends on the truth values of the simpler component statements. The component statements in a compound statement are often referred to as statement variables.
A compound statement usually consists of statement variables joined by logical connectives.
3. Logical Connectives:
Not (negation)
Mathematical symbol: ~
~p means "it is not the case that p" where p is some statement.
Other notations: EMBED Equation.DSMT4 , EMBED Equation.DSMT4
C++ notation:
The negation of a statement has the opposite truth-value from the statement. If p is true, ~p is false.
The definition of negation is displayed in a truth table
p ~p
F T
T F
And (conjunction)
Mathematical symbol: EMBED Equation.DSMT4
EMBED Equation.DSMT4 means “it is the case that p and q are true.”
C++ notation:
The conjunction of two statements p and q is true when and only when both p and q are both true.
The definition of conjunction is displayed in a truth table
p q EMBED Equation.DSMT4
F F
F T
T F
T T
Example
p: MIDN Berrios is an officer
q: MIDN
