Identity in Lattices
I'm having trouble proving this identity found in Curry's Foundations of Mathematical Logic.
Let $L$ be a lattice. For all $a,b,c,d in L$, show that:
$$(a wedge b) vee (c wedge d) leq (a vee c) wedge (b vee d) $$
I've tried to first show:
$$a wedge b leq (a vee c) wedge (b vee d)$$
$$ c wedge d leq (a vee c) wedge (b vee d)$$
but I'm getting nowhere.
Is this a good approach, or should I try something different?
Should I try finding a counter-example?
logic order-theory
asked Nov 25 '18 at 23:42
user458276
17119
add a comment |
I'm having trouble proving this identity found in Curry's Foundations of Mathematical Logic.
Let $L$ be a lattice. For all $a,b,c,d in L$, show that:
$$(a wedge b) vee (c wedge d) leq (a vee c) wedge (b vee d) $$
I've tried to first show:
$$a wedge b leq (a vee c) wedge (b vee d)$$
$$ c wedge d leq (a vee c) wedge (b vee d)$$
but I'm getting nowhere.
Is this a good approach, or should I try something different?
Should I try finding a counter-example?
logic order-theory
asked Nov 25 '18 at 23:42
user458276
17119
Great question. Keep it up.
– The Great Duck
Nov 25 '18 at 23:57
add a comment |
I'm having trouble proving this identity found in Curry's Foundations of Mathematical Logic.
Let $L$ be a lattice. For all $a,b,c,d in L$, show that:
$$(a wedge b) vee (c wedge d) leq (a vee c) wedge (b vee d) $$
I've tried to first show:
$$a wedge b leq (a vee c) wedge (b vee d)$$
$$ c wedge d leq (a vee c) wedge (b vee d)$$
but I'm getting nowhere.
Is this a good approach, or should I try something different?
Should I try finding a counter-example?
logic order-theory
asked Nov 25 '18 at 23:42
user458276
17119
I'm having trouble proving this identity found in Curry's Foundations of Mathematical Logic.
Let $L$ be a lattice. For all $a,b,c,d in L$, show that:
$$(a wedge b) vee (c wedge d) leq (a vee c) wedge (b vee d) $$
I've tried to first show:
$$a wedge b leq (a vee c) wedge (b vee d)$$
$$ c wedge d leq (a vee c) wedge (b vee d)$$
but I'm getting nowhere.
Is this a good approach, or should I try something different?
Should I try finding a counter-example?
logic order-theory
logic order-theory
asked Nov 25 '18 at 23:42
user458276
17119
asked Nov 25 '18 at 23:42
user458276
17119
asked Nov 25 '18 at 23:42
user458276
17119
asked Nov 25 '18 at 23:42
user458276
17119
asked Nov 25 '18 at 23:42
user458276
17119
17119
Great question. Keep it up.
– The Great Duck
Nov 25 '18 at 23:57
add a comment |
Great question. Keep it up.
– The Great Duck
Nov 25 '18 at 23:57
Great question. Keep it up.
– The Great Duck
Nov 25 '18 at 23:57
Great question. Keep it up.
– The Great Duck
Nov 25 '18 at 23:57
add a comment |
1 Answer
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$$aland ble ale alor c$$
$$aland ble ble blor d$$
$$aland ble alor cquad&quad aland ble blor dimplies aland ble(alor c)land(blor d)$$
answered Nov 25 '18 at 23:52
bof
50.3k457119
Thank you @bof!
– user458276
Nov 26 '18 at 2:05
add a comment |
Your Answer
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1 Answer
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1 Answer
1
active
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active
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active
oldest
votes
$$aland ble ale alor c$$
$$aland ble ble blor d$$
$$aland ble alor cquad&quad aland ble blor dimplies aland ble(alor c)land(blor d)$$
answered Nov 25 '18 at 23:52
bof
50.3k457119
Thank you @bof!
– user458276
Nov 26 '18 at 2:05
add a comment |
$$aland ble ale alor c$$
$$aland ble ble blor d$$
$$aland ble alor cquad&quad aland ble blor dimplies aland ble(alor c)land(blor d)$$
answered Nov 25 '18 at 23:52
bof
50.3k457119
Thank you @bof!
– user458276
Nov 26 '18 at 2:05
add a comment |
$$aland ble ale alor c$$
$$aland ble ble blor d$$
$$aland ble alor cquad&quad aland ble blor dimplies aland ble(alor c)land(blor d)$$
answered Nov 25 '18 at 23:52
bof
50.3k457119
$$aland ble ale alor c$$
$$aland ble ble blor d$$
$$aland ble alor cquad&quad aland ble blor dimplies aland ble(alor c)land(blor d)$$
answered Nov 25 '18 at 23:52
bof
50.3k457119
answered Nov 25 '18 at 23:52
bof
50.3k457119
answered Nov 25 '18 at 23:52
bof
50.3k457119
answered Nov 25 '18 at 23:52
bof
50.3k457119
50.3k457119
Thank you @bof!
– user458276
Nov 26 '18 at 2:05
add a comment |
Thank you @bof!
– user458276
Nov 26 '18 at 2:05
Thank you @bof!
– user458276
Nov 26 '18 at 2:05
Thank you @bof!
– user458276
Nov 26 '18 at 2:05
add a comment |
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Great question. Keep it up.
– The Great Duck
Nov 25 '18 at 23:57