##### evaluate exists 0<i<=length(x)  x[i]%%2==0 
E=function(x){
  E=FALSE
  if (is.vector(x)&& is.numeric(x)){
    for(i in 1:length(x)){
        E=(x[i]%%2==0 || E)
    }
  }    
  return(E)
}

x=c(1,2,3)
E(x)
x=c(1,5,3)
E(x)

any(x%%2==0)


##### evaluate for all 0<i<=length(x)  x[i]%%2==0 
A=function(x){
  A=TRUE
  if (is.vector(x)&& is.numeric(x)){
    for(i in 1:length(x)){
      A=(x[i]%%2==0 && A)
    }
  }    
  return(A)
}

x=c(1,2,3)
A(x)
x=c(2,4,12)
A(x)

all(x%%2==0)

##### evaluate exists 0<i<=nrow(m) s.t. for all  0<j<=ncol(m) m[i,j]%%2==0  
 EA=function(m){
  E=FALSE
  if (is.matrix(m)&& is.numeric(m)){
    for(i in 1:nrow(m)){
      A=TRUE
      for (j in 1:ncol(m))
        A=(m[i,j]%%2==0 && A)
      E=E||A
    }
  }    
return(E)
}

debug(EA)
m=matrix(c(1,3,3,4),ncol=2)
EA(m)
m=matrix(c(1,2,6,4),ncol=2)
EA(m)


##### evaluate for all 0<i<=nrow(m) exists  0<j<=ncol(m) s.t. m[i,j]%%2==0  
AE=function(m){
  A=TRUE
  if (is.matrix(m)&& is.numeric(m)){
    for(i in 1:nrow(m)){
      E=FALSE
      for (j in 1:ncol(m))
        E=(m[i,j]%%2==0 || E)
      A=A && E
    }
  }    
  return(A)
}

debug(AE)
m=matrix(c(1,3,2,4),ncol=2)
AE(m)
m=matrix(c(1,2,1,4),ncol=2)
AE(m)