Logical conjunction

Got it! This site "creationpie.com" uses cookies. You consent to this by clicking on "Got it!" or by continuing to use this website. Note: This appears on each machine/browser from which this site is accessed.

The English word "conjuction" comes, through French, from the Latin word "coniungere" ≈ "join".

The logical conjunction or intersection of two operands is true if (and only if) both operands are true. The logical conjunction "and" is the same as the natural language "and".

Example: To graduate, you must take and pass both MA101 (Math 101) and EN101 (English 101) and some others, ignored here. That is, you must take both courses to graduate.

Conjunction can be extended to any number of operators. There are other logical operators for two-valued logic that are not needed here.

More: Two-valued logic: Operators

The conjunction of two planets happens when the two planets are both in-line with the sun.

Example: Conjunction of Venus and the Earth.

Conjoined twins are born joined at some part of their body.

Job 38:31 Canst thou bind the sweet influences of Pleiades, or loose the bands of Orion? [kjv]

συνηκας δε δεσμον πλειαδος και φραγμον ωριωνος ηνοιξας [lxx]

… coniungere … Pliadis … Arcturi … [v]

The logical conjunction of two operands is true if (and only if) both operands are true. The English word "conjuction" comes, through French, from the Latin word "coniungere" ≈ "join".

The LXX (Septuagint) uses the word "and" for conjunction while the English uses "or" for disjunction. Most translations use the word "or" or omit any use of "and" or "or" (e.g., the NIV (New International Version)).

Job 38:31

All

KJV: Canst thou bind the sweet influences of Pleiades, or loose the bands of Orion?

Hebrew: התקשר מעדנות כימה או משכות כסיל תפתח׃

Greek: συνηκας δε δεσμον πλειαδος και φραγμον ωριωνος ηνοιξας

Latin: numquid coniungere valebis micantes stellas Pliadis aut gyrum Arcturi poteris dissipare

Wycliffe: Whether thou schalt mowe ioyne togidere schynynge sterris Pliades, ethir thou schalt mowe distrie the cumpas of Arturis?

Luther: Kannst du die Bande der sieben Sterne zusammenbinden, oder das Band des Orion auflösen?

Job 38:31 Canst thou bind the sweet influences of Pleiades, or loose the bands of Orion? [kjv]

συνηκας δε δεσμον πλειαδος και φραγμον ωριωνος ηνοιξας [lxx]

… coniungere … Pliadis … Arcturi … [v]

The constellation Orion and the Pleiades are more related than they appear in the sky.

Details are left as a future topic.

Logical expressions deal with how the logical values True and False are combined.

False And False is False
False And True is False
True And False is False
True And True is True

Some other symbols for And:

∧ (math notation), ∩ (set notation, intersection)
&& (C-based languages , & is the bitwise conjunction)
and (Python, Lua, Pascal, etc.)

The conjunction or intersection of A & B or A and B is true=1 if both of A and B are true=1, else the result is false=0.

Venn diagrams	Expression tree	Extended truth table
	$Expression tree for A & B$	A B \| A & B ----------- 0 0 \| 0 0 0 0 1 \| 0 0 1 1 0 \| 1 0 0 1 1 \| 1 1 1 The result is in the column under the "&" operator.

The word "and" is a conjunction in that both parts (on either side) are needed.

Example: You need to buy milk and cookies at the store.
Distribute as follows.

You need to buy milk at the store and
you need to buy cookies at the store.

You need to do both.

Logical conjunction (i.e., "And", "&", etc.) is related to the intersection operation of sets.

Here is a mathematical definition of set intersection.

Note how the set intersection operator "∩" and the logical conjunction symbol "∧" are related. They are wide at the bottom and narrow/close at the top. This did not just happen. They are related.

$Expression tree for A & B$	A B \| A & B ----------- 0 0 \| 0 0 0 0 1 \| 0 0 1 1 0 \| 1 0 0 1 1 \| 1 1 1 Here is the extended truth table using 0 for false and 1 for true.
Here is a tree diagram for the conjunction of logical values A and B. Values flow up the tree.	The result (under the operator "&") is true or 1 only if both A and B are 1 or true.

Short circuit evaluation comes from the idea that, logically, the conjunction of A and B is false if either A is false or B is false.

If one evaluates A and it is false, one need not even look at B to determine that the conjunction is false.

If one evaluates B and it is false, one need not even look at A to determine that the conjunction is false.

The order does not matter!

This follows a general principle in computer science and logic and reasoning that there are times when one can determine that one need not even bother (spend time) looking (which takes time and resources).

More: Nothing is something: actions