diagonal vs set

diagonal and set both are nouns.

Word	Noun	Adjective	Verb	Adverb
diagonal	Yes	Yes	No	No
set	Yes	Yes	Yes	No

As nouns, set is a hypernym of diagonal; that is, set is a word with a broader meaning than diagonal:

diagonal: (mathematics) a set of entries in a square matrix running diagonally either from the upper left to lower right entry or running from the upper right to lower left entry
set: (mathematics) an abstract collection of numbers or symbols

diagonal (noun)	set (noun)
a punctuation mark (/) used to separate related items of information	several exercises intended to be done in series
an oblique line of squares of the same color on a checkerboard	the act of putting something in position
(mathematics) a set of entries in a square matrix running diagonally either from the upper left to lower right entry or running from the upper right to lower left entry	representation consisting of the scenery and other properties used to identify the location of a dramatic production
a line or cut across a fabric that is not at right angles to a side of the fabric	any electronic equipment that receives or transmits radio or tv signals
(geometry) a straight line connecting any two vertices of a polygon that are not adjacent	(psychology) being temporarily ready to respond in a particular way
	a relatively permanent inclination to react in a particular way
	the descent of a heavenly body below the horizon
	a group of things of the same kind that belong together and are so used
	an unofficial association of people or groups
	(mathematics) an abstract collection of numbers or symbols
	the process of becoming hard or solid by cooling or drying or crystallization
	a unit of play in tennis or squash

diagonal (adjective)	set (adjective)
having an oblique or slanted direction	set down according to a plan
connecting two nonadjacent corners of a plane figure or any two corners of a solid that are not in the same face	being below the horizon
	converted to solid form (as concrete)
	fixed and unmoving
	(usually followed by `to' or `for') on the point of or strongly disposed
	situated in a particular spot or position
	determined or decided upon as by an authority

diagonal (verb)	set (verb)
	arrange attractively
	produce fruit
	alter or regulate so as to achieve accuracy or conform to a standard
	put into a certain state; cause to be in a certain state
	set to a certain position or cause to operate correctly
	equip with sails or masts
	become gelatinous
	make ready or suitable or equip in advance for a particular purpose or for some use, event, etc
	get ready for a particular purpose or event
	fix conclusively or authoritatively
	estimate
	decide upon or fix definitely
	establish as the highest level or best performance
	urge to attack someone
	put into a certain place or abstract location
	fix in a border
	give a fine, sharp edge to a knife or razor
	insert (a nail or screw below the surface, as into a countersink)
	put or set (seeds, seedlings, or plants) into the ground
	put into a position that will restore a normal state
	adapt for performance in a different way
	locate
	set in type
	apply or start
	disappear beyond the horizon