Using the truth table, examine whether the following statement pattern is tautology, contradiction and contingency.
$(p\wedge \sim q)\leftrightarrow (p\to q)$
Answer
363k+ views
Hint: Construct the truth table for $(p\wedge \sim q)\leftrightarrow (p\to q)$ and if all the propositions are true in every row then it is tautology, if all the propositions are false in every row then contradiction and if there is at least one row with true condition and one row with false condition, then it is contingency.
Complete step-by-step answer:
A truth table is a mathematical table used in logic- specifically in connection with Boolean algebra, Boolean functions and propositional calculus- which sets out the functional values of logical expressions on each of their functional arguments, that is for each combination of values taken by their logical variables. A truth table can be used to show whether a propositional expression is true for all input values, that is logically valid.
Tautology: A tautology has a logical form that cannot possibly be false no matter what truth values are assigned to the sentence letters.
Contradiction: A tautology has a logical form that cannot possibly be true no matter what truth values are assigned to the sentence letters.
Contingency: A Contingency has a logical form that can be either true or false depending on what truth values are assigned to the sentence letters.
Note: $p\wedge q$ is true when both $p$ and $q$ are true. $p\to q$ is true when $q$ is true or both are false. $p\leftrightarrow q$ is true when both $p$ and $q$ are true or both are false. This is the rule used to draw the above truth table.
Complete step-by-step answer:
A truth table is a mathematical table used in logic- specifically in connection with Boolean algebra, Boolean functions and propositional calculus- which sets out the functional values of logical expressions on each of their functional arguments, that is for each combination of values taken by their logical variables. A truth table can be used to show whether a propositional expression is true for all input values, that is logically valid.
Tautology: A tautology has a logical form that cannot possibly be false no matter what truth values are assigned to the sentence letters.
Contradiction: A tautology has a logical form that cannot possibly be true no matter what truth values are assigned to the sentence letters.
Contingency: A Contingency has a logical form that can be either true or false depending on what truth values are assigned to the sentence letters.

Note: $p\wedge q$ is true when both $p$ and $q$ are true. $p\to q$ is true when $q$ is true or both are false. $p\leftrightarrow q$ is true when both $p$ and $q$ are true or both are false. This is the rule used to draw the above truth table.
Last updated date: 29th Sep 2023
•
Total views: 363k
•
Views today: 6.63k
Recently Updated Pages
What do you mean by public facilities

Difference between hardware and software

Disadvantages of Advertising

10 Advantages and Disadvantages of Plastic

What do you mean by Endemic Species

What is the Botanical Name of Dog , Cat , Turmeric , Mushroom , Palm

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

How many millions make a billion class 6 maths CBSE

Find the value of the expression given below sin 30circ class 11 maths CBSE

Number of Prime between 1 to 100 is class 6 maths CBSE

Who had the title of Andhra Kavita Pitamaha A Nandi class 11 social science CBSE

How many crores make 10 million class 7 maths CBSE

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
