Consider the following predicates. P(x) is the statement "x−4<1". Q(x) is the statement "x+4⩽3". R(x) is the statement "x−4>0". Determine the truth value of the following propositions. P(8)→¬Q(−2) T or F? Q(3)∧¬R(3) T or F? R(5)→P(5) T or F?
Consider the following predicates.
P(x) is the statement "x−4<1".
Q(x) is the statement "x+4⩽3".
R(x) is the statement "x−4>0".
Determine the truth value of the following propositions.
P(8)→¬Q(−2) T or F?
Q(3)∧¬R(3) T or F?
R(5)→P(5) T or F?
Proposition is a statement that is either true or false. A proposition can be expressed in terms of predicates, which are mathematical expressions that define certain properties or relationships. The truth value of a proposition can be determined based on the truth values of its constituent predicates.
The symbols "→" and "∧" are logical operators that are used to combine propositions and form more complex propositions. The symbol "→" represents the conditional operator, and it is read as "if ... then ...," or simply "implies." The truth value of a proposition of the form "P→Q" is determined based on the truth values of P and Q, as follows:
- If P is True and Q is True, then the proposition "P→Q" is True.
- If P is True and Q is False, then the proposition "P→Q" is False.
- If P is False, then the proposition "P→Q" is True, regardless of the truth value of Q.
The symbol "∧" represents the logical operator "and," and it is used to form conjunctions, or propositions that are true only if all of their constituent propositions are true. The truth value of a proposition of the form "P∧Q" is True only if both P and Q are True, and False otherwise.
The symbol "¬" represents the logical operator "not," and it is used to form negations of propositions. The truth value of a proposition of the form "¬P" is the opposite of the truth value of P.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
