LOSTinDISCRETE
New member
- Joined
- Apr 23, 2010
- Messages
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#A = {x |x (is in) S ^ (?y)(y (is in) A --> x p y)}
A# = { x |x (is in) S ^ (?y)(y (is in) A --> y p x)}
a. Prove that if p is symmetric, then #A=A#
Suppose p is symmetric
If x p y --> y p x
Then x=x by antisymmetry
Then #A=A#
b. Prove that if A (is a subset) B then #B (is a subset) #A and B# (is a subset) A#
Suppose A (is a subset) B
Let x (be in) A and x (be in) B
-
-
#B (is a subset) #A and B# (is a subset) A#
c. Prove that A (is a subset) (#A)#
d. Prove that A (is a subset) #(A#)
I am lost on how to prove these problems. The way I started letter b is how I would start all of them. I do not know if this is correct or not. Can someone please help me. Thank you.
A# = { x |x (is in) S ^ (?y)(y (is in) A --> y p x)}
a. Prove that if p is symmetric, then #A=A#
Suppose p is symmetric
If x p y --> y p x
Then x=x by antisymmetry
Then #A=A#
b. Prove that if A (is a subset) B then #B (is a subset) #A and B# (is a subset) A#
Suppose A (is a subset) B
Let x (be in) A and x (be in) B
-
-
#B (is a subset) #A and B# (is a subset) A#
c. Prove that A (is a subset) (#A)#
d. Prove that A (is a subset) #(A#)
I am lost on how to prove these problems. The way I started letter b is how I would start all of them. I do not know if this is correct or not. Can someone please help me. Thank you.