diff --git a/logic/logicPlan.py b/logic/logicPlan.py
index 3d10afd..069be55 100644
--- a/logic/logicPlan.py
+++ b/logic/logicPlan.py
@@ -49,9 +49,10 @@ def sentence1() -> Expr:
     (not A) if and only if ((not B) or C)
     (not A) or (not B) or C
     """
-    "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
-    "*** END YOUR CODE HERE ***"
+    A=Expr('A')
+    B=Expr('B')
+    C=Expr('C')
+    return conjoin([A | B, (~A % ( ~B | C)), disjoin([~A , ~B , C])])
 
 
 def sentence2() -> Expr:
@@ -62,9 +63,8 @@ def sentence2() -> Expr:
     (not (B and (not C))) implies A
     (not D) implies C
     """
-    "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
-    "*** END YOUR CODE HERE ***"
+    A,B,C,D=Expr('A'),Expr('B'),Expr('C'),Expr('D')
+    return conjoin([(C % (B | D)), (A >> (~B & ~D)), (~(B & ~C) >> A), (~D >> C)])
 
 
 def sentence3() -> Expr:
@@ -79,9 +79,12 @@ def sentence3() -> Expr:
 
     Pacman is born at time 0.
     """
-    "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
-    "*** END YOUR CODE HERE ***"
+    PacmanAlive_0=PropSymbolExpr('PacmanAlive_0')
+    PacmanAlive_1=PropSymbolExpr('PacmanAlive_1')
+    PacmanBorn_0=PropSymbolExpr('PacmanBorn_0')
+    PacmanKilled_0=PropSymbolExpr('PacmanKilled_0')
+    # the answer should be "((PacmanAlive_1 <=> ((PacmanAlive_0 & ~PacmanKilled_0) | (~PacmanAlive_0 & PacmanBorn_0))) & ~(PacmanAlive_0 & PacmanBorn_0) & PacmanBorn_0)"
+    return conjoin([(PacmanAlive_1 % ((PacmanAlive_0 & ~PacmanKilled_0) | (~PacmanAlive_0 & PacmanBorn_0))), (~(PacmanAlive_0 & PacmanBorn_0)), PacmanBorn_0])
 
 def findModel(sentence: Expr) -> Dict[Expr, bool]:
     """Given a propositional logic sentence (i.e. a Expr instance), returns a satisfying
@@ -95,25 +98,20 @@ def findModelUnderstandingCheck() -> Dict[Expr, bool]:
     You should not use findModel or Expr in this method.
     """
     a = Expr('A')
-    "*** BEGIN YOUR CODE HERE ***"
-    print("a.__dict__ is:", a.__dict__) # might be helpful for getting ideas
-    util.raiseNotDefined()
-    "*** END YOUR CODE HERE ***"
+    a.__dict__['op']='a'
+    return {a:True}
 
 def entails(premise: Expr, conclusion: Expr) -> bool:
     """Returns True if the premise entails the conclusion and False otherwise.
     """
-    "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
-    "*** END YOUR CODE HERE ***"
+    expr=conjoin([premise,~conclusion])
+    return not pycoSAT(to_cnf(expr))
 
 def plTrueInverse(assignments: Dict[Expr, bool], inverse_statement: Expr) -> bool:
     """Returns True if the (not inverse_statement) is True given assignments and False otherwise.
     pl_true may be useful here; see logic.py for its description.
     """
-    "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
-    "*** END YOUR CODE HERE ***"
+    return pl_true(~inverse_statement,assignments)
 
 #______________________________________________________________________________
 # QUESTION 2