Here is a word study on Sanctify:

Websters 1828 dictionary:

sanctify

SANC'TIFY, v.t. [Low L. sanctifico; from sanctus, holy, and facio, to make.]

1. In a general sense, to cleanse, purify or make holy.

2. To separate, set apart or appoint to a holy, sacred or religious use.

God blessed the seventh day and sanctified it. Gen. 2.

So under the Jewish dispensation, to sanctify the altar, the temple, the priests, &c.

3. To purify; to prepare for divine service, and for partaking of holy things. Ex. 19.

4. To separate, ordain and appoint to the work of redemption and the government of the church. John 10.

5. To cleanse from corruption; to purify from sin; to make holy be detaching the affections from the world and its defilements, and exalting them to a supreme love to God.

Sanctify them through thy truth; thy word is truth. John 17. Eph. 5.

6. To make the means of holiness; to render productive of holiness or piety.

Those judgments of God are the more welcome, as a means which his mercy hath sanctified so to me, as to make me repent of that unjust act.

7. To make free from guilt.

That holy man amaz'd at what he saw, made haste to sanctify the bliss by law.

8. To secure from violation.

Truth guards the poet, sanctifies the line.

To sanctify God, to praise and celebrate him as a holy being; to acknowledge and honor his holy majesty, and to reverence his character and laws. Is. 8.

God sanctifies himself or his name, by vindicating his honor from the reproaches of the wicked, and manifesting his glory. Ezek. 36.

Scriptures:

Genisis 2:3

  3 And God blessed the ^aseventh day, and ^bsanctified it: because that in it he had ^crested from all his work which God ^dcreated and made.

• John 17:19

  19 And for their sakes I sanctify myself, that they also might be sanctified through the truth.
  
   Leviticus 21:8
  
  • 8 Thou shalt sanctify him therefore; for he offereth the bread of thy God: he shall be holy unto thee: for I the Lord, which sanctify you, am holy.
    
    Joshua 7:13
    
    • 13 Up, sanctify the people, and say, Sanctify yourselves against to morrow: for thus saith the Lord God of Israel, There is an accursed thing in the midst of thee, O Israel: thou canst not stand before thine enemies, until ye take away the accursed thing from among you.
      
      2 Chronicles 29:5
      
      • 5 And said unto them, Hear me, ye Levites, sanctify now yourselves, and sanctify the house of the Lord God of your fathers, and carry forth the filthiness out of the holy place.
      
      
      Quotes :
      
      “Sanctify yourselves: for to morrow the Lord will do wonders among you.”
      ~ Jeffery R. Holland
      
       "The Atonement of Jesus Christ is available to each of us. His Atonement is infinite. It applies to everyone, even you. It can clean, reclaim, and sanctify even you. That is what infinite means—total, complete, all, forever"
      ~ Shayne M. Bowen
      
      
      
      
      Personal Definition:
  • I think that what it means to Sanctify means to to clean, or cleanse or to make different.
  • When we are baptized we get sanctified. Same with when we take the sacrament each week, we sanctify ourselves. Same with repentance. We clean and make ourselves different in a good way. 
  • To change and be purer, and not repeat the same sin, and act on your purity and cleanness and be better because of it, I think is what it means to be truly Sanctified.
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Here's a word study on Ease:



Websters 1828 Dictionary:

ease

EASE, n. s as z. [L. otium.]

1. Rest; an undisturbed state. Applied to the body, freedom from pain, disturbance, excitement or annoyance. He sits at his ease. He takes his ease.

2. Applied to the mind, a quiet state; tranquillity; freedom from pain, concern, anxiety, solicitude, or any thing that frets or ruffles the mind.

His soul shall dwell at ease. Ps.25.

Wo to them that are at ease in Zion. Amos.6.

3. Rest from labor.

4. Facility; freedom from difficulty or great labor. One man will perform this service with ease. This author writes with ease.

5. Freedom from stiffness, harshness, forced expressions, or unnatural arrangement; as the ease of style.

6. Freedom from constraint or formality; unaffectedness; as ease of behavior.At ease, in an undisturbed state; free from pain or anxiety.

Scriptures: 

Mosiah 21:15

• Book of Mormon

And now the Lord was slow to hear their cry because of their iniquities; nevertheless the Lord did hear their cries, and began to soften the hearts of the Lamanites that they began to ease their burdens; yet the Lord did not see fit to deliver them out of bondage. 

Alma 39:17

• Book of Mormon

And now I will ease your mind somewhat on this subject. Behold, you marvel why these things should be known so long beforehand. Behold, I say unto you, is not a soul at this time as precious unto God as a soul will be at the time of his coming? 

Mosiah 24:15

• Book of Mormon

And now it came to pass that the burdens which were laid upon Alma and his brethren were made light; yea, the Lord did strengthen them that they could bear up their burdens with ease, and they did submit cheerfully and with patience to all the will of the Lord. 

Amos 6:

• Old Testament

AmosChapter 6Woe to them who are at ease in Zion—Israel will be plagued with desolation. 

Quotes:

.

 He that would live in peace and at ease must not speak all he knows or all he sees.
~Benjamin Franklin

Character cannot be developed in ease and quiet. Only through experience of trial and suffering can the soul be strengthened, ambition inspired, and success achieved.
~ Hellen Keller

 Try to be like the turtle - at ease in your own shell.
~Bill Copeland


My personal definition:
I think Ease has two different meanings. One I think means lazy, like you are to much at ease, so much as not to care about others. And the other meaning I think is deep peace. Like a relaxed sense, like it said "They were at ease because He lifted their burdens."
So there's this Ease: lazy, not caring of others and not doing anything, couch potato. 
And there's this Ease: peace, relaxed, burdens lifted, free, content.

I know that we can have both ease, but lets not be the lazy kind, lets be the serving kind, and we will still be at ease if we are serving, because He can ease our burdens. An there is a deep peace and Ease that comes with serving and doing His will. :)