Answer
Verified
39.9k+ 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.
Recently Updated Pages
Let gx 1 + x x and fx left beginarray20c 1x 0 0x 0 class 12 maths JEE_Main
The number of ways in which 5 boys and 3 girls can-class-12-maths-JEE_Main
Find dfracddxleft left sin x rightlog x right A left class 12 maths JEE_Main
Distance of the point x1y1z1from the line fracx x2l class 12 maths JEE_Main
In a box containing 100 eggs 10 eggs are rotten What class 12 maths JEE_Main
dfracddxex + 3log x A ex cdot x2x + 3 B ex cdot xx class 12 maths JEE_Main
Other Pages
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
The mole fraction of the solute in a 1 molal aqueous class 11 chemistry JEE_Main
How many grams of concentrated nitric acid solution class 11 chemistry JEE_Main
A closed organ pipe and an open organ pipe are tuned class 11 physics JEE_Main
Dissolving 120g of urea molwt60 in 1000g of water gave class 11 chemistry JEE_Main