diff --git a/logicPlan.py b/logicPlan.py
index 205e8c3..a6ab1a5 100644
--- a/logicPlan.py
+++ b/logicPlan.py
@@ -50,7 +50,15 @@ def sentence1() -> Expr:
     (not A) or (not B) or C
     """
     "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
+    A = Expr('A')
+    B = Expr('B')
+    C = Expr('C')
+    cond1 = A | B
+    cond2 = ~A % (~B | C)
+    cond3 = logic.disjoin(~A, ~B, C)
+
+    return logic.conjoin(cond1, cond2, cond3)
+
     "*** END YOUR CODE HERE ***"
 
 
@@ -63,7 +71,16 @@ def sentence2() -> Expr:
     (not D) implies C
     """
     "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
+    A = Expr('A')
+    B = Expr('B')
+    C = Expr('C')
+    D = Expr('D')
+    cond1 = C % (B | D)
+    cond2 = A >> (~B & ~D)
+    cond3 = ~(B & ~C) >> A
+    cond4 = ~D >> C
+
+    return logic.conjoin(cond1, cond2, cond3, cond4)
     "*** END YOUR CODE HERE ***"
 
 
@@ -80,7 +97,16 @@ def sentence3() -> Expr:
     Pacman is born at time 0.
     """
     "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
+    PacmanAlive_0 = PropSymbolExpr('PacmanAlive', time=0)
+    PacmanAlive_1 = PropSymbolExpr('PacmanAlive', time=1)
+    PacmanBorn_0 = PropSymbolExpr('PacmanBorn', time=0) 
+    PacmanKilled_0 = PropSymbolExpr('PacmanKilled', time=0)
+
+    cond1 = PacmanAlive_1 % ((PacmanAlive_0 & ~PacmanKilled_0) | (~PacmanAlive_0 & PacmanBorn_0))
+    cond2 = ~(PacmanAlive_0 & PacmanBorn_0)
+    cond3 = PacmanBorn_0
+
+    return logic.conjoin(cond1, cond2, cond3)
     "*** END YOUR CODE HERE ***"
 
 def findModel(sentence: Expr) -> Dict[Expr, bool]:
@@ -96,15 +122,27 @@ def findModelUnderstandingCheck() -> Dict[Expr, bool]:
     """
     a = Expr('A')
     "*** BEGIN YOUR CODE HERE ***"
-    print("a.__dict__ is:", a.__dict__) # might be helpful for getting ideas
-    util.raiseNotDefined()
+
+    class dummyClass():
+        def __init__(self, expr: Expr):
+            self.name = expr.__dict__['op'].lower()
+
+        def __repr__(self):
+            return self.name
+
+    return {dummyClass(a): True}
+    
     "*** END YOUR CODE HERE ***"
 
 def entails(premise: Expr, conclusion: Expr) -> bool:
     """Returns True if the premise entails the conclusion and False otherwise.
     """
     "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
+    # 如果 前提成立，但是（結論不成立） -> 代表 entails 不成立
+    check = premise & ~conclusion
+
+    return False if findModel(check) else True
+
     "*** END YOUR CODE HERE ***"
 
 def plTrueInverse(assignments: Dict[Expr, bool], inverse_statement: Expr) -> bool:
@@ -112,7 +150,8 @@ def plTrueInverse(assignments: Dict[Expr, bool], inverse_statement: Expr) -> boo
     pl_true may be useful here; see logic.py for its description.
     """
     "*** BEGIN YOUR CODE HERE ***"
-    util.raiseNotDefined()
+    return pl_true(~inverse_statement, assignments)
+
     "*** END YOUR CODE HERE ***"
 
 #______________________________________________________________________________