# Answer to Question #58540 in Functional Programming for Melody

Question #58540

1. When the following are true? The following symbols are used:

~ - negation,

v – disjunction,

& - conjunction,

-> - implication

1. p & ~p v q

2. ~(x v y) = ~x & ~y

3. ~( a -> ~b)

For each of the following, under what circumstances are they TRUE

For example, question 1 is true only when q is true

TRUE 1, FALSE 0

This is about boolean logic

Conjunction: a AND b, a ∩ b, a & b, a && b

True only if both a and b are true

Disjunction: a OR b, a ∪ b, a || b ,

False only if both a and b are false

Negation: NOT a

True only if a is false

Implication: a IMPLIES b

False only when a true and b false

Equivalence: a IS EQUIVALENT TO b, a = b, a == b ,

True when a and b are the same

~ - negation,

v – disjunction,

& - conjunction,

-> - implication

1. p & ~p v q

2. ~(x v y) = ~x & ~y

3. ~( a -> ~b)

For each of the following, under what circumstances are they TRUE

For example, question 1 is true only when q is true

TRUE 1, FALSE 0

This is about boolean logic

Conjunction: a AND b, a ∩ b, a & b, a && b

True only if both a and b are true

Disjunction: a OR b, a ∪ b, a || b ,

False only if both a and b are false

Negation: NOT a

True only if a is false

Implication: a IMPLIES b

False only when a true and b false

Equivalence: a IS EQUIVALENT TO b, a = b, a == b ,

True when a and b are the same

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