Question

a) Lets p, q, r represent the following statements: p: it is hot today. q: it is sunny r: it is raining Express in words the statements using Bicondtional statement represented by the following formulas: i. q ↔ p ii. p ↔ ( q ˄ r ) iii. p ↔ ( q ˅ r) iv. r ↔ ( p ˅ q)

Answer 1

Explanation:

The arrow with two tips is translated as "if and only if". The symbols
`\land, \lor` and read as "and" and "or"respectively.

If we have the following p: it is hot today. q: it is sunny r: it is raining

Then

i. q ↔ p : It is sunny if and only if it is hot today.

ii. p ↔ ( q ˄ r ) : it is hot today if and only if it is sunny and it is raining

iii. p ↔ ( q ˅ r) : it is hot today if and only if it is sunny or it is raining

iv. r ↔ ( p ˅ q) : it is raining if and only if it is hot today or it is sunny