1 thought on “If p, q, r have truth values T. F. T. respectively then what is the truth value of [(~pVq) ^r]?”
[tex] \bf \: The \: truth \: table \: of \: \sim \: (p \: \lor \: q) \: \land \: r \: is \: [/tex]
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c|c|c} \bf p & \bf q& \bf r & \bf \sim \: p& \bf \sim \: p \lor \: q& \bf (\sim \: p \lor \: q) \land \: r\\ \frac{\qquad}{} & \frac{\qquad}{}& \frac{\qquad}{} & \frac{\qquad}{}& \frac{\qquad}{}& \frac{\qquad}{}\\ \sf T & \sf T & \sf T& \sf F& \sf T& \sf T\\ \\\sf T & \sf T & \sf F& \sf F& \sf T& \sf F\\ \\\sf T & \sf F & \sf T& \sf F& \sf F& \sf F\\ \\\sf T & \sf F & \sf F& \sf F& \sf F& \sf F\\ \\\sf F & \sf T & \sf T& \sf T& \sf T& \sf T\\ \\\sf F & \sf T & \sf F& \sf T& \sf T& \sf F\\ \\\sf F & \sf F & \sf T& \sf T& \sf T& \sf T\\ \\\sf F & \sf F & \sf F& \sf T& \sf T& \sf F\\ \\ \sf & \sf \end{array}} \\ \end{gathered}[/tex]
So,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c|c|c} \bf p & \bf q& \bf r & \bf \sim \: p& \bf \sim \: p \lor \: q& \bf (\sim \: p \lor \: q) \land \: r\\ \frac{\qquad}{} & \frac{\qquad}{}& \frac{\qquad}{} & \frac{\qquad}{}& \frac{\qquad}{}& \frac{\qquad}{}\\ \sf T & \sf F & \sf T& \sf F& \sf F& \sf F\\\end{array}} \\ \end{gathered}[/tex]
Basic Concept :-
A truth table is a mathematical table used to determine if a compound statement is true or false. In a truth table, each statement is typically represented by a letter or variable, like p, q, or r, and each statement also has its own corresponding column in the truth table that lists all of the possible truth values.
A disjunction is a compound statement representing the word ‘or.’
A conjunction is a compound statement representing the word ‘and.’
The negation of a statement, called not p, is the statement that contradicts p and has the opposite truth value.
[tex] \bf \: The \: truth \: table \: of \: \sim \: (p \: \lor \: q) \: \land \: r \: is \: [/tex]
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c|c|c} \bf p & \bf q& \bf r & \bf \sim \: p& \bf \sim \: p \lor \: q& \bf (\sim \: p \lor \: q) \land \: r\\ \frac{\qquad}{} & \frac{\qquad}{}& \frac{\qquad}{} & \frac{\qquad}{}& \frac{\qquad}{}& \frac{\qquad}{}\\ \sf T & \sf T & \sf T& \sf F& \sf T& \sf T\\ \\\sf T & \sf T & \sf F& \sf F& \sf T& \sf F\\ \\\sf T & \sf F & \sf T& \sf F& \sf F& \sf F\\ \\\sf T & \sf F & \sf F& \sf F& \sf F& \sf F\\ \\\sf F & \sf T & \sf T& \sf T& \sf T& \sf T\\ \\\sf F & \sf T & \sf F& \sf T& \sf T& \sf F\\ \\\sf F & \sf F & \sf T& \sf T& \sf T& \sf T\\ \\\sf F & \sf F & \sf F& \sf T& \sf T& \sf F\\ \\ \sf & \sf \end{array}} \\ \end{gathered}[/tex]
So,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c|c|c} \bf p & \bf q& \bf r & \bf \sim \: p& \bf \sim \: p \lor \: q& \bf (\sim \: p \lor \: q) \land \: r\\ \frac{\qquad}{} & \frac{\qquad}{}& \frac{\qquad}{} & \frac{\qquad}{}& \frac{\qquad}{}& \frac{\qquad}{}\\ \sf T & \sf F & \sf T& \sf F& \sf F& \sf F\\\end{array}} \\ \end{gathered}[/tex]
Basic Concept :-
A truth table is a mathematical table used to determine if a compound statement is true or false. In a truth table, each statement is typically represented by a letter or variable, like p, q, or r, and each statement also has its own corresponding column in the truth table that lists all of the possible truth values.