# October 10th
# boolean functions - return False or True

## is it a forall-relation, or a there-exists relation
## forall - and ,  there-exists - or

# is there a negative number in the array
def findneg(A):
    ax = False  # default value for a there-exists relation
    i = 0
    while i<=len(A)-1 and not(ax):  #ax==False:
        if (A[i] < 0): ax = True
        i += 1
    # while
    return ax

# forall :checks if an array of integers is sorted [2,4,7,9]->True
# [2,4,7,5,9]  -> False  :  if not(A[i] <= A[i+1])
def sorted(A):
    ax = True # for-all relation default
    i = 0
    while i<= len(A)-2 and ax:
        if (A[i] > A[i+1]): ax = False
        i += 1
    # while
    return ax

def myin(x,A):  # True if x is in array A
    ax = False
    i =0
    while i<len(A) and not(ax):
        if x==A[i]: ax = True
        i += 1
    return ax

# subset relation A subset B
def sublist(A,B): # True if all elements of A are in B
    ax = True
    i = 0
    while i<len(A) and ax==True:
        if not(myin(A[i],B)): ax = False
        i += 1
    # while
    return ax

def sublist2(A,B):
    ax = True
    i = 0 # outer loop counter
    while i<len(A)and ax:
        # compare A[i] against everything in B
        ax = False  # inner loop accumulator
        j = 0  # inner loop counter
        while j<len(B) and ax==False: #not(ax):
            if A[i] == B[j]: ax = True
            j += 1
        # while j inner loop
        #if not(bx): ax = False
        #ax = bx
        i +=1
    # while i outer loop
    return ax



## boolean function: test if two arrays are disjoint
# disjoint([2,4,1],[3,5,4,7])  --> False
def disjoint(A,B):
    i = 0
    ax = True   # ax,bx,cx,dx  eax ebx ecx rax rbx rcx
    while i<len(A) and ax:
        if not(A[i] in B): ax = False
        i+=1

    #while
    return ax