Checking If Cons exist in list of Cons - lisp

Question

I am building a program and lisp and need to check if a Cons exist in a list of cons, but for some reason it keep returning nil in the if statement, here is the current code I am using for it.
(defun countVertexTriangles (graph numOfVertices)
(findTriangle graph numOfVertices)
)
(defun findTriangle(graph numOfVertices)
(loop for (x y) in graph do
(loop for z from 1 to numOfVertices do
(write graph)
(terpri)
(write (cons z (cons y nil)))
(terpri)
(write (cons z (cons x nil)))
(terpri)
; (if (AND (member (cons z (cons y nil)) graph) (member (cons z (cons x nil)) graph))
; then (write (cons y z))
; )
)
(terpri)
)
)
; (defun findEdge(graph edge)
; (loop for x in graph do
; (write x)
; (write edge)
; (if (eql x edge)
; (write "A")
; (write "B")
; )
; )
; )
(defun testFunct ()
(setf g1 '((1 2)(2 3)(1 3)(2 4)(3 4)(4 5)(3 5)))
(countVertexTriangles g1 5)
)
(testFunct)
Why does the member(cons z (cons y nil)) return nil even when in the first iteration we can see (1 2) exists in the list?
Edit:
Currently even when it is true it returns nil, why would this be the case given the following code?
(defun countVertexTriangles (graph numOfVertices)
(findTriangle graph numOfVertices)
)
(defun findTriangle(graph numOfVertices)
(loop for (x y) in graph do
(loop for z from 1 to numOfVertices do
; (write graph)
; (terpri)
; (write (list z y ))
; (terpri)
(write (findEdge graph (list z y)))
(terpri)
; (if (AND (member (list z x) graph) (member (list z x ) graph))
; then (write "TEST")
; )
)
(terpri)
)
)
(defun findEdge(graph edge)
(loop for x in graph do
(if (equal x edge)
(return-true)
(return-false)
)
)
)
(defun return-true ()
t)
(defun return-false ()
nil)
(defun testFunct ()
(setf g1 '((1 2)(2 3)(1 3)(2 4)(3 4)(4 5)(3 5)))
(countVertexTriangles g1 5)
)

Answer 1

findEdge doesn't return anything. Calling return-true and return-false doesn't return from findEdge. You also shouldn't return until you find a match.
(defun findEdge(graph edge)
(loop for x in graph do
(if (equal x edge)
(return-from findEdge (return-true))
)
)
(return-false)
)
This can be simplified to just:
(defun findEdge (graph edge)
(member edge findEdge :test #'equal))