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Logic

  

Equivalent

  

test for logical equivalence

  

Implies

  

test for logical implication

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Equivalent(a, b, p)

Implies(a, b, p)

Parameters

a, b

-

Boolean expressions

p

-

(optional) unevaluated name

Description

• 

The Equivalent and Implies commands test the Boolean expressions a and b for logical equivalence or logical implication respectively.

• 

The Equivalent(a, b) calling sequence returns true in the event that the two expressions are logically equivalent, and false if they are not.  Similarly, Implies(a, b) returns true if a implies b (that is, if for every valuation for which a is true, then b is also true) and false otherwise.

• 

If the parameter p is supplied and the test returns false, then a valuation is assigned to p which demonstrates a negative result.  Otherwise, p is assigned NULL.

  

Note: The test may be significantly faster if p is not given.

Examples

withLogic:

Equivalenta&anda&orb,a

true

(1)

Equivalenta&iffa&orb,b&impliesa

true

(2)

Equivalenta&impliesb,b&impliesa,p

false

(3)

p

a=false,b=true

(4)

Equivalent&nota&andb,&nota&or&notb,p

true

(5)

p

a&andba&impliesb

true

(6)

a&xorba&andb&or&nota&or&notb

true

(7)

Impliesb&impliesa&impliesc,a&iffb&orb&andc,p

false

(8)

p

a=false,b=true,c=false

(9)

Impliesa&orb,a&or&notb,p

false

(10)

p

a=false,b=true

(11)

See Also

Logic

Logic/Satisfy

Logic/Tautology