How to reduce this if statement?-CodePudding

if(year@0==0 || (year0!=0 && year%4==0))

statement is in the form of a or (b' and c)

Does this reduce to a or (b or c') ?

if(year@0==0 || (year0==0 || year%4!=0))

Is there a mistake in this reduction? (I thought it was correct but these two does not give the same results.)

CodePudding user response：

Does this reduce to a or ( b or c' )?

No. You can see this by building a truth table.

We can change the and to an or.

  b' and c
= ( b' and c )''
= ( b or c' )'

a or ( b' and c )

becomes

a or ( b or c' )'

Not useful, except to show it's not equivalent to a or ( b or c' ).

We can change the and to an or using the same approach.

a or ( b' and c )

becomes

( a' and ( b or c' ) )'

Again, not useful.

It can be simplified to year % 4 == 0, as long as you only deal with the years 1901 to 2099.

CodePudding user response：

Consider the example of year = 100. Your first statement will return false, while the second will return true.

The second or statement enclosed in parentheses does not need to be, and so can be considered as a simple check of the three conditions individually.