#' Logical implies

Returns the result of \(x\Longrightarrow y\).

implies(x, y)

x %implies% y

Arguments

x, y	Logical vectors of the same length.

Value

Logical implies: TRUE unless x is TRUE and y is FALSE.

NA in either x or y results in NA if and only if the result is unknown. In particular NA %implies% TRUE is TRUE and FALSE %implies% NA is TRUE.

If x or y are length-one, the function proceeds as if the length-one vector were recycled to the length of the other.

Examples

library(data.table)
CJ(x = c(TRUE,
         FALSE),
   y = c(TRUE,
         FALSE))[, ` x => y` := x %implies% y][]
#>        x     y  x => y
#> 1: FALSE FALSE    TRUE
#> 2: FALSE  TRUE    TRUE
#> 3:  TRUE FALSE   FALSE
#> 4:  TRUE  TRUE    TRUE

#>        x     y  x => y
#> 1: FALSE FALSE    TRUE
#> 2: FALSE  TRUE    TRUE
#> 3:  TRUE FALSE   FALSE
#> 4:  TRUE  TRUE    TRUE

# NA results:
#> 5:    NA    NA      NA
#> 6:    NA FALSE      NA
#> 7:    NA  TRUE    TRUE
#> 8: FALSE    NA    TRUE
#> 9:  TRUE    NA      NA